Mixture Fraction Probability Density Function Research Articles

Model Comparisons of Flow and Chemical Kinetic Mechanisms for Methane–Air Combustion for Engineering Applications

The reasonably accurate numerical simulation of methane–air combustion is important for engineering purposes. In the present work, the validations of sub-models were carried out on a laboratory-scale turbulent jet flame, Sandia Flame D, in comparison with experimental data. The eddy dissipation concept (EDC), which assumes that the molecular mixing and subsequent combustion occur in the fine structures, was used for the turbulence–chemistry interaction. The standard k-ε model (SKE) with the standard or the changed model constant C1ε, the realizable k-ε model (RKE), the shear-stress transport k-ω model (SST), and the Reynolds stress model (RSM) were compared with the detailed chemical kinetic mechanism of GRI-Mech 3.0. Different reaction treatments for the methane–air combustion were also validated with the available experimental data from the literature. In general, there were good agreements between predictions and measurements, which gave a good indication of the adequacy and accuracy of the method and its further applications for industry-scale turbulent combustion simulations. The differences between predictions and measured data might have come from the simplifications of the boundary settings, the turbulence model, the turbulence–reaction interaction, and the radiation heat transfer model. For engineering predictions of methane–air combustion, the mixture fraction probability density function (PDF) model for the partially premixed combustion with RSM is recommended due to its relatively low simulation expenses, acceptable accuracy predictions, and quantitatively good agreement with the experiments.

Large Eddy Simulation on the Effects of Coal Particles Size on Turbulent Combustion Characteristics and NOx Formation Inside a Corner-Fired Furnace

Abstract The effects of pulverized coal particles’ sizes on the coal combustion characteristics are numerically studied in a laboratory-scale tangentially fired furnace. The turbulent gas flow and the coal particle motion are solved by employing the large eddy simulation (LES) and the discrete phase model (DPM). The mixture fraction probability density function (MF-PDF) is coupled to simulate the non-premixed pulverized coal combustion. It is found that the coal combustion efficiency is positively affected by the dispersion of coal powders. The particle dispersion and the coal combustion are augmented by the intensive impingement caused by the corner-injected flow. Large coal particles, with their greater inertia, enhance particle agglomerations, which limit the combustion of volatile and char. Accordingly, the average flame temperature decreases with the growing particle sizes. Also, the O2 concentration increases slightly because of the incomplete coal combustion, and the CO2 concentration decreases gradually. In contrast, the CO concentration increases markedly in the furnace center due to the presence of a reducing atmosphere. The NO concentration exhibits an exponential decline with the increased particle size. A relatively stable combustion and a relatively low NOx formation are acquired inside such a corner-fired furnace when the particle Stokes number is a little greater than 1.

Application of quadrature-based moment methods to the conditional moment closure

Two solution algorithms are developed for the conditional moment closure (CMC) using quadrature-based moment methods (QBMM). Their primary purpose is to eliminate the necessity of the additional grid for the conditioning variable (e.g., mixture fraction). As in almost every probability-density-function (PDF)-based description, the main technical hurdle is the solution of the molecular-mixing term. Here the focus is on solving this term coupled with chemistry, as opposed to spatial transport. In the first algorithm (referred to as SA-CMC), this is done by semi-analytically solving an equation for the deviation variable of the conditional scalar mean in terms of Jacobi polynomials. The mixture-fraction space is represented by the Gauss–Lobatto quadrature rule and a β-PDF. In the second algorithm (referred to as QBMM-CMC), a closed set of differential equations is written for the joint moments of a scalar and the mixture fraction, thereby eliminating the need to assume a form for the mixture-fraction PDF. Both solution algorithms are tested for multi-step H2 combustion, and the expected results are achieved with at most six quadrature nodes. Since in the proposed algorithms the scalar mean is ensured to be constant during molecular mixing, it is further concluded that the proposed algorithms are accurate, computationally cost-effective, and straightforward alternatives for traditional CMC solution methods.

A quadrature-based conditional moment closure for mixing-sensitive reactions

A novel algorithm consisting of a quadrature-based semi-analytical solution to the conditional moment closure (CMC) is developed for mixing-sensitive reactions in turbulent flows. When applying the proposed algorithm, the additional grid in mixture-fraction phase space used in CMC codes is eliminated, and at most ten quadrature nodes are needed to model mixing-sensitive turbulent reacting flows. In this work, the mixture-fraction probability density function (PDF) is assumed to be a β-PDF, which is the weight function for the Gauss-Jacobi quadrature rule. The conditional moments of reacting species are determined from unconditional moments that are first order with respect to the species and higher order with respect to mixture fraction. Here, the focus is on the efficient treatment of the molecular-mixing step by using a semi-analytical solution in the form of a Jacobi polynomial expansion. The application of the algorithm is demonstrated considering mixing-sensitive competitive-consecutive and parallel reactions in a statistically homogeneous chemical reactor.

Coupling RSM with soot model for the study of soot formation in a momentum-dominated strained jet flames

This paper presents a comparison between the numerically determined soot volume fraction (SVF) in a momentum-dominated turbulent diffusion strained jet flames burning ethylene/hydrogen/nitrogen mixture in air with experimental results. The soot inception model used is based on the formation rate of two or three ring poly aromatic hydrocarbon with C6H6 as the soot precursor. Second-moment closure Reynolds stress method turbulent model is used in conjunction with the governing equation of mass, momentum and energy. The turbulent combustion kinetic chemistry interaction is modeled by choosing a chemical equilibrium non-premixed combustion model along with the species inlet diffusion probability density function (PDF). Soot radiation source term like P-1 radiation model is also included along with the turbulent combustion model. The soot turbulence interaction invoked uses single-variable PDF based on the temperature and mixture fraction (Z) for measurement of flame lift-off height, flame length and radiative heat loss. Equilibrium-based Lee soot oxidation model is chosen to estimate the hydroxyl (OH) and O2 species for the oxidation of soot particles. The numerical solutions for each of the experimental configurations are proposed by Mahmoud and co-workers for three different strained flames (4000 s−1, 7300 s−1, and 12,900 s−1). In each discretized finite volume cell, using a quadratic upstream interpolation for convective kinematics algorithm in spatial coordinate and time-bounded second-order accurate in temporal coordinate solution is obtained. All the above turbulence combustion interaction models are iterated with unit Courant–Friedrichs–Lewy condition. It is noted that the mixture fraction (Z) PDF used is very sensitive to the chosen turbulence combustion soot interaction models. Also, it is observed that the simulated outputs are in good agreement with the measured experimental data in terms of SVF, temperature both axially and radially. SVF increases with a decrease in the flame strain rate and shows the reverse trend in radially integrated soot volume reaction. In agreement with experiments, soot productivity shows a linear relationship in momentum-dominated flame with an increase in the strain rates for soot productivity, maximum mean SVF, exit Froude number, exit C2H4 flow rate.

Large eddy simulation of non-premixed pulverized coal combustion in corner-fired furnace for various excess air ratios

• The pulverized-coal combustion of corner-fired furnace is simulated by LES . • The influences of excess air ratio on coal combustion are investigated. • The flame characteristic and the dispersed burning particles are studied. • The NO x emissions generated at various atmospheres are compared. Large-eddy simulations (LES) were carried out to study the effects of burning atmosphere on the coal combustion process in a corner-fired furnace. The LES for the turbulent gas was coupled with the discrete phase model (DPM) for coal particles trajectories and the non-premixed mixture fraction probability density function (MF-PDF) combustion model for pulverized coal combustion . The coal combustion processes, including the flame characteristics, burning coal behaviors and NO x pollutant emissions, for different burning atmospheres are analyzed qualitatively and quantitatively. The heat and momentum transfer between burning coal and turbulent gas are greatly enhanced by the corner-fired flow. With a given particle size, the char particles present a similar distribution in the whole chamber. For a fuel-rich atmosphere, the concentration is obviously much higher and exhibits much higher spatial variability than the other two conditions. The coal combustion efficiency decreases in oxygen-rich and fuel-rich burning atmospheres, but the flame stability is more affected at the fuel-rich atmosphere by the lack of oxygen. NO pollutant is obviously reduced at the fuel-rich atmospheres, and the NO pollutant emissions are more affected by the reducing atmosphere than the low temperature. These findings may provide insight into strategies to design and monitor tangentially-fired pulverized coal boilers.

Evaluation of mixture-fraction-based turbulent-reaction-rate model assumptions for high-pressure reactive flows

Several assumptions of atmospheric-pressure (atmospheric-p) single-phase turbulent reaction rate models are examined for high-p reactive flows having turbulent characteristics. The study uses a Direct Numerical Simulation (DNS) database described elsewhere (Bellan, 2017). This database was obtained with a model combining multi-species mixing under high- p conditions, a real-gas equation of state (EOS) and a single-step chemical reaction. The database, created in the configuration of a temporal mixing layer, probes the effect of the initial Reynolds number, Re0, of the initial pressure, p0, and of the initial composition of the two mixing-layer streams. The reaction is initiated in a turbulent flow and in each simulation the computations are pursued past a time when a maximum average-volumetric p is attained, tpp*. The examination of the vorticity and enstrophy equations at a time before reaction initiation and also at tpp* highlights the pivotal role of the high density-gradient magnitude regions (Bellan, 2017) in producing turbulence and the crucial role at tpp* of the baroclinic effect representing the misalignments of gradients of thermodynamic variables. Compared to the classical mixture fraction equation, the results show that the mixture fraction obeys an equation in which there is an additional diffusion term having a larger r.m.s. magnitude than that of the mixture-fraction typical diffusion term. An assessment of the Conditional Source-term Estimation (CSE) model assumptions found that, using an accurate mixture fraction probability density function (PDF), one can obtain a very good representation of the turbulent reaction rate in the most intense reaction regions, however the quality of the predictions of CSE deteriorated significantly when a common model for the PDF, the β -PDF, was used despite the β-PDF being constructed with the accurate moments extracted from the DNS. In the regions of minimal reaction, the CSE model using the exact PDF extracted from the DNS does not provide an accurate representation of the turbulent reaction rate, a fact which is attributed to the combined effect of lack of correlation between fluctuations of the reaction rate and of the mixture fraction, and to the strong correlation of the thermodynamic variables through the real-gas EOS in regions of colder and denser fluid.

Application of Flame Speed Closure Model to RANS Simulations of Stratified Turbulent Combustion in a Gasoline Direct-Injection Spark-Ignition Engine

ABSTRACTThe present work aims at development and validation of a tool for numerically modeling stratified turbulent combustion in a gasoline direct injection (GDI) engine. For this purpose, an open source code called OpenFOAM®, which has been attracting growing interests from both industries and academies due to an opportunity to access the source code and to test new models without paying license fees, is further developed by implementing advanced models relevant to stratified turbulent burning. In particular, first, the Flame Speed Closure model of premixed turbulent combustion is implemented in order to simulate flame propagation through inhomogeneously premixed reactants. Second, a newly calculated approximation of the laminar flame speed of gasoline-air mixtures as a function of the equivalence ratio, pressure, and temperature is implemented in order to simulate dependence of burning rate on the local mixture composition. Third, a newly calculated approximation of the combustion temperature of gasoline-air mixtures as a function of the equivalence ratio, pressure, and product enthalpy is implemented in order to allow for dissociation of combustion products and heat losses. Fourth, a presumed mixture-fraction probability density function (PDF) approach is implemented in order to simulate the influence of turbulent fluctuations in the mixture fraction on the local burning rate. In addition to commonly used mass-weighted mixture-fraction PDF, a more consistent model that deals also with the canonical mixture-fraction PDF is developed and the two approaches are compared. Numerical results that show the influence of the aforementioned implementations on computed global characteristics of stratified combustion in a research GDI engine are discussed. The developed numerical tool is quantitatively validated by comparing computed pressure traces in the GDI engine with experimental data obtained in three different cases associated with two different loads, late injection timings, and short time intervals between the injection and spark ignition.

Modeling of Pulverized Coal Combustion in Turbulent Flow with the Consideration of Intermediate Reactions of Volatile Matter

The eddy dissipation concept (EDC) model with the consideration of the intermediate reactions for the volatile matter (VM) combustion was applied to simulate turbulent pulverized coal/air jet combustion adjacent to a bluff-boy type model burner. The VM of the coal was assumed to consist of CO, H2, and CH4, and its chemistry was described by a 16-speices and 41-step skeletal mechanism for CH4/air combustion. The model was compared with some other conventionally used ones, including the eddy dissipation (ED) model, eddy dissipation or finite rate (ED-FR) model, mixture fraction probability density function (MF-PDF) model, and the EDC model with a global reaction mechanism for gas phase combustion (EDC_G), in predicting temperature profiles, maximum flame temperature, flame shape, and ignition position and in CPU cost. The predicted temperature profiles and flame positions were further compared with reported experimental data. It was found that the EDC model with the consideration of the intermediate reactions for VM combustion improved prediction in the temperature field and thus ignition position. With the adoption of the full in situ adaptive tabulation (ISAT) method, two-third of the overall CPU time could be saved, making the EDC model more acceptable in comparison with the ED-type models and MF-PDF model. On the basis of the simulation results, it is suggested that intermediate reactions of the VM should be considered when high accuracy of flame temperature and ignition position prediction is desired in simulation of pulverized coal combustion.

The large eddy simulation of a turbulent diffusion flame

Internal structure of a turbulent diffusion flame (Sandia Flame D) has been investigated numerically by means of CFD code Ansys Fluent 6.3. For this flame, detailed measurements are currently available. In the simulations, two strategies of turbulence modeling (large eddy simulation and Reynolds-Favre averaging) jointly with two approaches to model turbulent combustion (the mixture fraction probability density function model and the eddy dissipation model) have been applied. Comparisons of the simulation results with the available measurement data made it possible to identify the most adequate methodology for modeling turbulent diffusion jet flame.

Turbulent mixing in three-dimensional droplet arrays

The atomisation, evaporation and subsequent mixing of fuel from a liquid spray determines the effectiveness of the combustion processes in gas turbines and internal combustion engines. In the present paper, three-dimensional direct numerical simulations (DNS) of the evaporation of methanol droplets in hot environments are presented. The gas phase mixing is assessed by examining the scalar dissipation and the mixture fraction probability density function (PDF). Novel multi-conditional models are proposed that use mixture fraction and structural parameters as the conditioning variables for the scalar dissipation which is found to be well predicted in terms of magnitude and distribution. The β-PDF description of the mixture fraction seems to capture well the global behaviour for a laminar environment and for time-averaged results in turbulent cases. A novel model for the mixture fraction PDF is also proposed based on the multi-conditional model for scalar dissipation and an accurate representation of the PDF is achieved.

Comparison of Micromixing Models for Calculation of the Chemical Reaction Rate in Homogeneous Turbulent Flow

AbstractTurbulent mixing with a single second‐order isothermal reaction in a homogeneous flow is considered. A mixing model is stated using the probability density function (PDF) equation method and the concepts of mixture fraction and progress variable. Different micromixing models are compared. With the interaction exchange mean/linear square mean estimation (IEM/LSME) model, the time variation of the mixture fraction PDF contradicts the physical representation of mixing. The Langevin model describes mixing from the segregating state to the homogeneous state of a mixture. The PDF model proves to be two‐mode at intermediate mixing stages. This is also true for the multi‐zone PDF model. As compared to the multi‐zone PDF model, others reveal higher averaged progress variables over the entire time range and at all Damköhler number values. Such a difference is made by the approximations for the averaged reaction rate that should be allowed for in the modeling of turbulent mixing with chemical reaction.

Modeling of scalar mixing in turbulent jet flames by multiple mapping conditioning

Multiple mapping conditioning (MMC) combines the probability density function (PDF) and the conditional moment closure (CMC) methods via the application of a generalized mapping function to a prescribed reference space. Stochastic and deterministic formulations of MMC exist, and the deterministic implementation has been applied here to a piloted jet diffusion flame (Sandia Flame D). This paper focuses on the feasibility of MMC and its closures for real (laboratory) flames and a relatively simple one-dimensional reference space that represents mixture fraction has been used. The remaining chemically reactive species are implicitly conditioned on mixture fraction and their fluctuations around the conditional mean are neglected. This work primarily evaluates the ability of the deterministic form of MMC to provide accurate and consistent closures for the mixture fraction PDF and the conditional scalar dissipation which do not rely on presumed shape functions for the PDF such as the commonly used β-PDF. Computed probability distributions agree well with measurements, and a detailed comparison of the modeled conditional and mean scalar dissipation with experimental data and conventional closures demonstrate MMC’s potential. Predictions of reactive species and temperature are in good agreement with experimental data and similar in quality to singly conditioned, first-order CMC predictions. MMC therefore provides an attractive-since consistent-alternative approach for the modeling of scalar mixing in turbulent reacting flows.

Laser-Based Experimental and Monte Carlo PDF Numerical Investigation of an Ethanol/Air Spray Flame

A turbulent ethanol spray flame is characterized through quantitative experiments using laser-based imaging techniques. The experimental data set is used to validate a numerical code for the simulation of spray combustion. The spray burner has been constructed to facilitate the computational treatment of the experiment; in particular the spray flame is stabilized without a bluff body or a pilot flame. The experiments include spatially resolved measurements of droplet sizes (Mie/LIF-dropsizing and PDA), droplet velocity (PDA), liquid-phase temperature (two-color LIF temperature imaging with Rhodamine B) and gas-phase temperature (multi-line NO-LIF temperature imaging). The measurements close to the nozzle exit are used to determine the initial conditions for numerical simulations. A novel probability density function (PDF) method is applied to calculate the development of the spray flame. A joint mixture fraction and enthalpy PDF is formulated. Its transport equation is modeled and solved using a Monte-Carlo method. A detailed ethanol/air combustion mechanism consisting of 38 species and 337 elementary reactions is implemented through the spray flamelet model enabling the prediction of pollutant emission in spray flames. Good agreement with the experimental data is found for the gas temperature. The numerical predictions for the liquid-phase temperature are in reasonable agreement with the experimental data. The flame structure with two reaction zones is compared with other spray flames, and it is analyzed with the help of the experimental and numerical results. The formation mechanism of such a structure is revealed.

Simulation of a turbulent spray flame using coupled PDF gas phase and spray flamelet modeling

A joint mixture fraction–enthalpy probability density function (PDF) is proposed for the simulation of turbulent spray flames. The PDF transport equation is deduced and modeled. The interaction-by-exchange-with-the-mean (IEM) model that has been developed for gas-phase flows is extended to describe molecular mixing in nonreactive and reactive spray flows. The joint PDF transport equation is solved by a hybrid finite-volume and Lagrangian Monte Carlo method. Standard spray and turbulence models are used to describe the gas phase and the liquid phase. A turbulent methanol/air spray flame is simulated using the present method. Detailed chemistry is implemented through the spray flamelet model. The precalculated spray flamelet library for methanol/air combustion comprises 23 species and 168 elementary reactions. Thus, the model is capable of predicting the formation of radicals and of pollutants. Different values for the model constant C ϕ in the IEM model are tested. The numerical results for the gas velocity, the gas temperature, and the mass fraction of methanol vapor are compared with experimental data in the literature. Good agreement with experiment is obtained when C ϕ = 2.0 . Marginal PDFs of mixture fraction, enthalpy, and gas temperature are presented. The computed PDFs of mixture fraction are compared with the presumed standard β function and modified β function. The results show that the standard β function fails to reproduce bimodal shapes observed in transported PDF computation, while the modified β function, fits the computed PDFs very well. Moreover, joint PDFs of mixture fraction and enthalpy are presented and analyzed. The enthalpy and mixture fraction are strongly correlated. The samples that deviate from the linear correlation are due to the energy consumption of local spray evaporation.

Eulerian transported probability density function sub-filter model for large-eddy simulations of turbulent combustion

Reactive flow simulations using large-eddy simulations (LES) require modelling of sub-filter fluctuations. Although conserved scalars like mixture fraction can be represented using a beta-function, the reactive scalar probability density function (PDF) does not follow an universal shape. A one-point one-time joint composition PDF transport equation can be used to describe the evolution of the scalar PDF. The high-dimensional nature of this PDF transport equation requires the use of a statistical ensemble of notional particles and is directly coupled to the LES flow solver. However, the large grid sizes used in LES simulations will make such Lagrangian simulations computationally intractable. Here we propose the use of a Eulerian version of the transported-PDF scheme for simulating turbulent reactive flows. The direct quadrature method of moments (DQMOM) uses scalar-type equations with appropriate source terms to evolve the sub-filter PDF in terms of a finite number of delta-functions. Each delta-peak is characterized by a location and weight that are obtained from individual transport equations. To illustrate the feasibility of the scheme, we compare the model against a particle-based Lagrangian scheme and a presumed PDF model for the evolution of the mixture fraction PDF. All these models are applied to an experimental bluff-body flame and the simulated scalar and flow fields are compared with experimental data. The DQMOM model results show good agreement with the experimental data as well as the other sub-filter models used.

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.

Finite-rate chemistry effects in turbulent opposed flows: comparison of Raman/Rayleigh measurements and Monte Carlo PDF simulations

This study reports results from experimental and numerical investigations of a partially premixed turbulent opposed methane/air jet flame. Experimentally determined properties of the scalar and the flow field are compared to the results from a Monte Carlo simulation. One-dimensional spatially resolved Raman/Rayleigh scattering serves to quantify the mean species concentrations and temperature, whereas laser Doppler velocimetry is used to measure axial and radial velocity components. The simulation is simplified by using a one-dimensional formulation. It includes a Reynolds-stress turbulence model and a Monte Carlo simulation of the joint scalar probability density function (PDF). A non-uniform Monte Carlo particle distribution is used to minimize stochastic errors. The flame is operated close to extinction with strong interactions between turbulence and chemistry. Comparisons between experimental and numerical results reveal a good agreement of mixture fraction profiles along the centreline. However, species scatter plots and mixture fraction PDFs show discrepancies between experiment and simulation. Numerical simulations over-predict the extinction limits and therefore under-predict the intermittent nature of turbulence and mixing of the scalars.

A joint SSPDF–CMC method for simulating turbulent methane–air jet combustion

A joint single scalar probability density function and conditional moment closure (SSPDF–CMC) method is proposed for modeling a turbulent methane–air jet flame. In general, the probability density function (PDF) of passive scalar (such as mixture fraction) is non-Gaussian and not fully determined by the advecting velocity field, therefore the presumed shape of PDF of mixture fraction assumed as clipped Gaussian distribution or beta function in normal conditional moment closure (CMC) method is incorrect. In SSPDF–CMC method, the PDF of mixture fraction is obtained using a Monte-Carlo method to solve a PDF transport equation. An assumption that the averaged scalar advection is approximately equal to the averaged scalar dissipation in the wake of a grid-generated turbulence flow is adopted to model the averaged scalar dissipation. The predictions using the proposed method are compared with those using the conventional CMC method and the experimental data. It is seen that the predicted Favre conditional averaged statistics and Favre unconditional averaged statistics using the proposed method are in better agreement with the measurement data than those using the conventional CMC method. The predicted conditional or unconditional mean NO even using the SSPDF model is only in fair agreement with the experiments. It shows that the first-order closure for the conditional reaction rate of NO should be improved.

Identification of local extinction topology in axisymmetric bluff-body diffusion flames with a reactedness-mixture fraction presumed probability density function model

The effects of finite-rate chemistry, such as partial extinctions and re-ignitions, are investigated in turbulent non-pre-mixed reacting flows stabilized in the wake of an axisymmetric bluff-body burner. A two-dimensional large-eddy simulation procedure is employed that uses a partial equilibrium/two-scalar reactedness mixture fraction probability density function (PDF) combustion sub-model, which is applied at the sub-grid scale (SGS) level. An anisotropic sub-grid eddy–viscosity and two equations for the SGS turbulence kinetic and scalar energies complete the SGS closure model. The scalar covariances required in the joint PDF formulation are obtained from an extended scale-similarity assumption between the resolved and the sub-grid fluctuations. Extinction due to strong turbulence/chemistry interactions is recognized with the help of a ‘critical’, locally variable, turbulent Damkohler number criterion, while transient localized extinctions and re-ignitions are treated with a Lagrangian transport equation for a reactedness progress variable. Comparisons with available experimental data suggested that the formulated approach was capable of identifying the effects of large-scale vortex structure activity, which were inherent in the reacting wake and dominant in the counterpart isothermal flows that otherwise would have been obscured if a standard time-averaged procedure had been used. Additionally, the post-extinction and re-ignition behaviour and its time-varying interaction with the large-scale structure dynamics were more appropriately addressed within the context of the present time-dependent method. Copyright © 2001 John Wiley & Sons, Ltd.