Multiple Mapping Conditioning Research Articles

Effects of Partial Premixing and Coflow Temperature on Flame Stabilization of Lifted Jet Flames of Dimethyl Ether in a Vitiated Coflow Based on Stochastic Multiple Mapping Conditioning Approach

The Reynolds-averaged Navier–Stokes (RANS)-based stochastic multiple mapping conditioning (MMC) approach has been used to study partially premixed jet flames of dimethyl ether (DME) introduced into a vitiated coflowing oxidizer stream. This study investigates DME flames with varying degrees of partial premixing within a fuel jet across different coflow temperatures, delving into the underlying flame structure and stabilization mechanisms. Employing a turbulence k-ε model with a customized set of constants, the MMC technique utilizes a mixture fraction as the primary scalar, mapped to the reference variable. Solving a set of ordinary differential equations for the evolution of Lagrangian stochastic particles’ position and composition, the molecular mixing of these particles is executed using the modified Curl’s model. The lift-off height (LOH) derived from RANS-MMC simulations are juxtaposed with experimental data for different degrees of partial premixing of fuel jets and various coflow temperatures. The RANS-MMC methodology adeptly captures LOH for pure DME jets but exhibits an underestimation of flame LOH for partially premixed jet scenarios. Notably, as the degree of premixing escalates, a conspicuous underprediction in LOH becomes apparent. Conditional scatter and contour plots of OH and CH2O unveil that the propagation of partially premixed flames emerges as the dominant mechanism at high coflow temperatures, while autoignition governs flame stabilization at lower coflow temperatures in partially premixed flames. Additionally, for pure DME flames, autoignition remains the primary flame stabilization mechanism across all coflow temperature conditions. The study underscores the importance of considering the degree of premixing in partially premixed jet flames, as it significantly impacts flame stabilization mechanisms and LOH, thereby providing crucial insights into combustion dynamics for various practical applications.

A consistent MMC-LES approach for turbulent premixed flames

A multiple mapping conditioning (MMC) approach is coupled with large eddy simulations (LES) for the prediction of the flame propagation, the flame structure and finite rate chemistry effects including NO formation in turbulent premixed flames. The mixing term in MMC relies on a reference field that characterizes the chemical composition within the flame and it is typically taken to be the reaction progress variable. In LES, this reference field needs to be artificially thickened to be resolved on the LES grid. A novel MMC mixing time scale model that had been developed with the aid of direct numerical simulation (DNS), has been adapted to account for the thickening of the reference field. Equally, the particle selection mechanism for particle mixing has been modified to ensure localness of mixing in composition space and to preserve the prediction of a realistic (thin) flame thickness by the stochastic particles. A set of freely propagating turbulent premixed flames with varying equivalence ratios is used to test the performance of the MMC model. Results of MMC-LES are compared with reference DNS that include full chemistry. Additional simulations were carried out where MMC is coupled with quasi-DNS where the flow field is fully resolved but the reaction progress variable field is thickened and its source term is closed with a flamelet approach. This allows to isolate the different modelling assumptions invoked in MMC-LES. Deviations from the exact solution can then be associated with the MMC approach and with thickening of the reference field separately and they are small. The MMC-LES predictions of the turbulent premixed flame propagation speed and flame structure are very good and finite rate chemistry effects can be captured well which is demonstrated by good agreement of predicted NO with DNS data.

A DNS evaluation of three MMC-like mixing models for transported PDF modelling of turbulent nonpremixed flames

Transported probability density function (TPDF) methods are suitable for modelling turbulent reactive flows. One of the main challenges is to accurately model the molecular mixing terms. In TPDF mixing models, it is desired that the principle of localness is satisfied so that the molecular mixing is performed locally in both physical and composition spaces. The multiple mapping conditioning (MMC) mixing model can ensure mixing localness without violating other desired principles. The present study examines three MMC-like mixing models, including the original MMC (OMMC) mixing model, shadow-position mixing model (SPMM) and a conceptually simplified multiple mapping conditioning (SMMC) mixing model. Three direct numerical simulation (DNS) datasets modelling turbulent nonpremixed ethylene flames with increasing levels of extinction are used for model evaluation. The DNS datasets are also used to provide both initial conditions and inputs needed over the course of TPDF runs to remove the uncertainties caused by turbulence closure, allowing the study to focus on the molecular mixing model. The mixing model coefficients are specified analytically by reference to a canonical mean scalar gradient (MSG) flow in order to achieve specifiable dissipation rate and user-controllable localness. The results show that the MMC-like mixing models yield similar prediction of flame extinction and reignition if the coefficients are properly specified. The MMC-like mixing models can also be tuned to achieve a desired level of localness. For conditional statistics, the MMC-like mixing models can yield correct level of conditional variances. By changing localness, the MMC-like models can yield solutions resembling the interaction by exchange with the mean (IEM) or Euclidean minimum spanning tree (EMST) mixing model for extreme parameter choices. The models differ in their abilities to specify unconditional dissipation rates, at least in the flow considered, and in their ease of implementation.

Effects of pressure on the structure of partially premixed turbulent diffusion flames: Calculations using MMC-LES

This study numerically investigates the detailed structure of twelve partially premixed turbulent diffusion flames of methane and air across a pressure range between 1 and 20 bar. The flames are computed using the multiple mapping conditioning / large eddy simulations (MMC-LES) approach. The model is first validated against available experimental data at atmospheric pressure. This is followed by simulations of a series of flames with increasing pressure while holding either the bulk jet velocity or the jet Reynolds number constant. Results show that local extinction increases as pressure increases in cases with fixed bulk jet velocity. Meanwhile, an instability induced by body forces gradually arises as pressure increases at constant Reynolds number, but can be mitigated by reducing the gravitational acceleration, and hence the body forces, proportional to the pressure increase. Consequently, flames become more stable with less localised extinction when increasing pressure at constant Reynolds number. The study accurately reflects the effects of finite-rate chemistry with increasing pressure, as evidenced in representative plots of a Damköhler number ratio. Additionally, the approach to blow-off at different pressures is examined, and trends in temperature and species are analysed. The calculations presented in this study align well with existing data at atmospheric pressure and provide reliable blind test results that await detailed comparison with measurements not yet available at high pressures.

Characterizing the SpraySyn burners with MMC-LES

This paper presents a detailed validation of a modeling framework and its implementation for the simulation of flame spray pyrolysis (FSP) using different nozzle geometries of the so-called SpraySyn burner. Gas, liquid and particulate dynamics are compared against experimental data from literature as well as our own laser-Doppler anemometry, phase-Doppler anemometry and multi-line OH laser-induced fluorescence thermometry imaging measurements. The modeling framework consists of large eddy simulations (LES) coupled to the sparse-Lagrangian multiple mapping conditioning (MMC) model, a Lagrangian spray solver and a sectional description of the population balance equation. Simulations start downstream of the burner exit planes where turbulent inlet data for the gas and liquid phases are generated by independent LES that use a 1-Fluid method to capture the dynamics of the liquid jet break-up. The gas and liquid dynamics are validated and analyzed for an ethanol spray flame in the SpraySyn1 and SpraySyn2 burners. In these burners iron(III) oxide particulates are synthesized from iron pentacarbonyl (IPC)-ethanol solutions with varying IPC concentrations. The results demonstrate the very good predictive capabilities of the MMC modeling framework for the gas and liquid phases. The predictions of the particulate formation are validated by comparison of elastic light scattering (ELS) signals from experiments against synthetic ELS signals calculated from the simulations. Results are of reasonable accuracy for the SpraySyn1 FSP series but indicate an imbalance between particulate growth and dilution with the surrounding gas. Predictions for the SpraySyn2 FSP series are consistent with SpraySyn1 results and indicate an increased product particulate size due to an increased residence time downstream of the heat release zone.

MMC-LES of spray combustion: Analysis of mixing timescales and flame structure

Large-eddy simulations (LES) of turbulent, pilot-stabilised, dilute acetone spray flames are performed using the sparse-Lagrangian multiple mapping conditioning approach (MMC-LES). The primary objective of this work is to assess the adaptability of the recently proposed dynamically evaluated molecular mixing timescale model for MMC-LES (Sharma et al., 2022, A fully dynamic mixing timescale model for the sparse Lagrangian multiple mapping conditioning approach, Combustion and Flame, 238, 111872), referred to as the dyn-aISO model, to the non-reacting and reacting two-phase flows. This work is the first application to perform a dynamic evaluation of the mixing timescale for turbulent spray combustion using the transported filtered density function (FDF) approach. A non-reacting case and four reacting flames with varying fuel mass loading are investigated, where the flame transitions from a diffusion flame to a premixed flame structure with a decrease in fuel loading. As is conventional for MMC-LES, a sparse resolution of one stochastic particle per six Eulerian finite-volume cells is used in this study, offering a much cheaper computing expense than the conventional transported FDF approach. The liquid evaporation is represented based on a non-equilibrium model at the droplet surface. The reaction chemistry is based on an augmented GRI 3.0 mechanism containing 39 species and 226 reactions to represent the oxidation of acetone. Predictions with the dyn-aISO model are compared with the constant coefficient anisotropic mixing time scale model and the isotropic C-K model. Thorough validation of liquid-phase statistics and gas-phase temperature is performed with available experimental data and popular studies from the literature. Analysis of the flame structure, with different timescale models, for both non-premixed and premixed type flames is also carried out. Quantification of the parameters affecting the timescale, such as model constants of the sub-Lagrangian-grid scale (slgs) mixture fraction variance (Cf) and its scalar dissipation rate (Scsgs−1Cν) is provided in comparison to their conventionally chosen static coefficient values. Predictions with the dyn-aISO model are quite good for the diffusion-type flames, while some discrepancies are noticed while predicting a premixed flame structure for lower liquid loading case having near stoichiometric jet-exit mixture composition.

Investigation of elastic light scattering in flame spray pyrolysis modelled by a stochastic particle approach

The synthesis of iron(III) oxide particulates from iron pentacarbonyl (IPC) in a flame spray pyrolysis process is predicted by a multiple mapping conditioning (MMC) method. MMC is coupled with carrier-phase large eddy simulations and a sectional description of the population balance equation. MMC is a sparse particle method, where the number of stochastic particles is heavily reduced in comparison to conventional particle methods. The associated computational savings allow for the use of a detailed chemical mechanism for gas phase reactions, particulate precursor formation and an accurate description of the particulate size distribution. The numerical configuration is based on the SpraySyn burner which is a laboratory-scale burner for the synthesis of nano-particulates from liquid precursor solutions. The IPC concentration is varied from 0.2 mol/l to 0.8 mol/l IPC in ethanol to provide a series of validation experiments for the model’s prediction of particulate formation and growth. Parameter studies reveal that standard assumptions with respect to the morphology unduly affect the model’s prediction and that variation within sensible boundaries can significantly improve agreement with measurements and has large effects on the predicted particulate size distribution of the product species.

The hierarchy of low-dimensional manifolds in the context of multiple mapping conditioning mixing model

A new model to couple the multiple mapping conditioning (MMC) mixing model with manifold based simplified chemistry is proposed. The concept is based on the fact that the system state can be locally confined to a manifold with lower dimension, which is embedded in the manifold with higher dimension. Therefore, in the framework of the MMC mixing model, particles to be mixed must be selected such that they are localized in the reference variable space with the dimension which corresponds to the minimum number of the progress variables describing the thermo-kinetic states locally. This can be achieved by comparing the physical mixing time-scale with the chemical time-scales describing the movement on the slow manifold, and the dimension of the necessary reference variables can be determined automatically. The present work uses an IEM-based MMC mixing model and Reaction-Diffusion Manifolds (REDIMs) as the simplified chemistry, but it can be extended easily to other mixing models. The proposed methodology is validated by testing the well-known non-premixed Sandia Flame D and F, and the results show good agreement with experimental results and those obtained using the detailed chemistry.

Multiple Mapping Conditioning Mixing Time Scales for Turbulent Premixed Flames

A novel multiple mapping conditioning (MMC) mixing time scale model for turbulent premixed combustion has been developed. It combines time scales for the flamelet and distributed flame regimes with the aid of a blending function. The blending function serves two purposes. Firstly, it helps to identify zones where the premixed flame resides and where the time scale associated with the premixed flame shall be used. Secondly, it uses the Karlovitz number to identify the turbulent premixed combustion regime and to reduce the weighting of the premixed flame time scale if Karlovitz numbers are high and deviations from the flamelet regime are expected. A series of three-dimensional direct numerical simulations (DNS) of statistically one dimensional, freely propagating turbulent methane-air flames provides a wide range of turbulent combustion regimes for the mixing model validation. The new mixing time scale provides correct predictions of the flame speed of freely propagating turbulent flames which could not be matched by most recognized mixing models. The turbulent flame structure predicted by the new model is in good agreement with DNS for all combustion regimes from flamelet to the thickened reaction zone.

A coupled MMC-LES and sectional kinetic scheme for soot formation in a turbulent flame

A soot kinetic sectional scheme is coupled with the sparse multiple mapping conditioning / large eddy simulation (MMC-LES) method to model soot formation in a turbulent, non-premixed, piloted methane flame (Delft Flame III). The kinetic sectional scheme used here discretises the population balance equation according to soot particle size. The sections (or bins) are treated as lumped species, and the physico-chemical soot formation is modelled through elementary-like reaction pathways with Arrhenius rate expressions. This allows the soot kinetics to be naturally coupled with the gas phase molecular kinetics. Interactions of soot formation and molecular chemistry with turbulence is achieved through the MMC-LES model. This is a Monte Carlo filtered density function approach in which the micromixing is local in an independent reference space permitting use of a computationally efficient sparse distribution of stochastic notional particles. The model results are compared to experimental data for the gas-phase velocity and molecular species in the upstream low-soot region and with soot statistics in the downstream region. The gaseous quantities have very good agreement with the experimental data. Overall the soot predictions are in good qualitative agreement with the data, particularly with respect to the peak value of the mean soot volume fraction, the shape and range of the joint probability density function of soot volume fraction and spatial location, and the rate of soot oxidation and burnout. However, in common with other published attempts at the Delft Flame III using a range of different models, the predicted soot formation begins and peaks well upstream of the experimental measurements. The minimum soot intermittency is underpredicted relative to the data but shows a significant improvement on previous attempts to model it. The analysis also explores the evolution of the mean and instantaneous particle size distributions and some aspects of soot-chemistry-turbulence interactions.

A fully dynamic mixing time‐scale model for the sparse Lagrangian multiple mapping conditioning approach

Multiple mapping conditioning / large eddy simulation (MMC-LES) is a promising model for turbulence-chemistry interactions, successfully applied to simulate different combustion regimes involving gaseous, liquid, and solid fuels. MMC-LES attempts to produce accurate molecular mixing by localising mixing in an independent, composition-like reference space. In the MMC mixing model, mixing between two stochastic particles is defined based on the Lagrangian mixing time-scale τL, which is defined as the ratio of the Lagrangian subgrid-scale mixture fraction variance (fL′2˜) and the scalar dissipation rate (χL), typically modelled algebraically, based on fixed values of global constants at all spatial locations. Accurate modelling of τL is essential towards predicting the conditional scalar fluctuations, which is otherwise highly challenging if the same set of static constants are used at all spatial locations for complex flames with varying extinction/re-ignition. Herein, a fully dynamic mixing time-scale model (dyn-aISO) is proposed within the MMC-LES framework, which dynamically evaluates fL′2˜ and χL, essentially based on a local variance coefficient and variable turbulent Schmidt number, respectively, eliminating the need for specifying tuneable model constants. This novel dyn-aISO model is used to simulate the pilot-stabilised Sandia flame series with increasing local extinction levels. The conditional and unconditional profiles of compositional scalars from the new dynamic model are compared with those from a fully static model (st-aISO) and a model which uses a static constant for fL′2˜ (stCf-aISO). Numerical results from different timescale models deviate from each other for Sandia flame F having a high jet Reynolds number. With the proposed improvement of the micro-mixing time-scale model, the dyn-aISO model accurately captures the transient behaviour of the complete flame series, which could otherwise be obtained by the tuning of static constants. The role of molecular and turbulent mass diffusivities, coefficient of residual variance of mixture fraction, mixing distance, and the mixing time-scale on the predictions of the reactive scalars is also explored.

Large eddy simulation of a supersonic lifted hydrogen flame with sparse-Lagrangian multiple mapping conditioning approach

The Multiple Mapping Conditioning / Large Eddy Simulation (MMC-LES) approach is used to simulate a supersonic lifted hydrogen jet flame, which features shock-induced autoignition, shock-flame interaction, lifted flame stabilization, and finite-rate chemistry effects. The shocks and expansion waves, shock-reaction interactions and overall flame characteristics are accurately reproduced by the model. Predictions are compared with the detailed experimental data for the mean axial velocity, mean and root-mean-square temperature, species mole fractions, and mixture fraction at various locations. The predicted and experimentally observed flame structures are compared through scatter plots of species mole fractions and temperature against mixture fraction. Unlike most past MMC-LES which has been applied to low-Mach flames, in this supersonic flame case pressure work and viscous heating are included in the stochastic FDF equations. Analysis indicates that the pressure work plays an important role in autoignition induction and flame stabilization, whereas viscous heating is only significant in shear layers (but still negligibly small compared to the pressure work). The evolutions of particle information subject to local gas dynamics are extracted through trajectory analysis on representative fuel and oxidizer particles. The particles intermittently enter the extinction region and may be deviated from the full burning or mixing lines under the effects of shocks, expansion waves and viscous heating. The chemical explosive mode analysis performed on the Lagrangian particles shows that temperature, the H and OH radicals contribute dominantly to CEM respectively in the central fuel jet, fuel-rich and fuel-lean sides. The pronounced particle Damköhler numbers first occur in the fuel jet / coflow shear layer, enhanced at the first shock intersection point and peak around the flame stabilization point.

Coupling the Multiple Mapping Conditioning Mixing Model with Reaction-diffusion Databases in LES of Methane/air Flames

ABSTRACT The Multiple Mapping Conditioning (MMC) model for sparse Lagrangian Large-Eddy Simulations (LES) is coupled with tabulated chemistry based on reaction-diffusion manifolds (REDIM). In addition to assessing the reduction in computational cost compared to direct integration on the fly, a comparison with the previously implemented REDIM solver based on the Eulerian Stochastic Fields (ESF) is performed. The methane/air Sandia flames D and E are selected as a benchmark, which are amenable to a 2D REDIM database having a passive scalar and one progress variable as dimensions. A comparison between direct integration ESF and MMC shows that the latter gives better predictions of the conditional means and fluctuations, offering at the same time a significantly reduced computational cost. When coupled with REDIM, MMC and ESF models provide similar results, indicating the significant sensitivity of the predictions to the thermochemical states which are restricted to the same REDIM manifold. When the states are projected back onto the REDIM surface in the direction where the progress variables remain almost constant, accuracy is lost in the cold fuel-lean region with MMC. Furthermore, the computational performance gain in MMC compared to ESF is reduced when the REDIM tabulation is used, pointing to non-chemistry related computational bottlenecks in the MMC algorithms.

Parametric sensitivities of the generalized binomial Langevin–multiple mapping conditioning model

The binomial Langevin model (BLM) predicts mixture fraction statistics including higher moments excellently, but imposing boundedness for the large scalar spaces typically associated with chemically reacting flows becomes intractable. This central difficulty can be removed by using the mixture fraction as the reference variable in a generalized multiple mapping conditioning (MMC) approach. The resulting probabilistic BLM–MMC formulation has several free parameters that impact the turbulence–chemistry interactions in complex flows: the dissipation timescale ratio, the locality in selecting pairs of particles for mixing, and the fraction of particles mixed per time step. The impact of parametric variations on the behavior of the BLM–MMC model is investigated for a complex flow featuring auto-ignition to determine model sensitivities and identify optimal values. It is shown that only the mixture fraction rms is sensitive to the dissipation timescale ratio with the expected behavior of an increased ratio leading to a reduction in rms. Controlling locality by increasing the maximum possible distance between paired particles in reference space has a similar impact. Increasing the fraction of particles mixed only affects reacting scalars by advancing ignition. The modified Curl's model is used for the mixing process and the specified amount of mixing principally controls the local extinction and reignition behavior. It is further shown that the standard value of the dissipation timescale ratio is satisfactory; the amount of mixing should be half that specified by Curl's model; and the distance between particle pairs in reference space should be proportional to the diffusion length scale.

Modelling of a turbulent premixed flame series using a new MMC-LES model with a shadow position reference variable

A new multiple mapping conditioning model with a shadow position reference variable for localising mixing is implemented in a large eddy simulation solver and validated against three experimental turbulent premixed flames. The shadow position used here has diffusion coefficient which is linked to the turbulent propagation speed. Localisation of mixing produces a flamelet-like inner structure in shadow position space and the structure in physical space is determined by the subgrid dispersion of shadow and physical positions. The lengths of the predicted flames match the trends observed for the experimental flames, and the predicted inner structures are consistent with what is expected for these flames in the thin reaction zones regime. The statistical predictions are in very good quantitative agreement with the experimental data for velocity and major species. Errors for reaction progress variable, turbulent kinetic energy and minor species (carbon monoxide) are generally larger yet mostly within the ranges reported in the literature.

Application of the sparse-Lagrangian multiple mapping conditioning approach to a model supersonic combustor

The Multiple Mapping Conditioning/Large Eddy Simulation (MMC-LES) model is extended for the first time to high-speed, compressible flow conditions and validated against non-reacting and reacting experimental data from a model supersonic combustor. The MMC-LES method solves the subgrid joint composition filtered density function through a Monte Carlo approach, and it permits a low-cost numerical implementation using a sparse distribution of stochastic Lagrangian particles. The sensitivity of results to the particle resolution is examined, and similar to past low-speed applications of MMC-LES, that sensitivity is found to be low. In comparison to the model equations for subsonic turbulent combustion conditions, the pressure work and viscous heating effects have been incorporated here to account for the effects of compressibility. As expected, the viscous heating effects are small for this flow case and can be ignored, while the pressure work is not negligible and makes a significant contribution at expansion fans and shock fronts where the magnitude of the pressure derivative term in non-reacting/reacting cases is as much as 23.8%/24.5% and 19.2%/18.6% of the stochastic particle standardized enthalpy, respectively. The MMC-LES predictions show good quantitative agreement with the available experimental data for the mean and root-mean-square of axial velocity, mean temperature, and wall pressure. Good qualitative comparison to the data is also observed for major flow characteristics, including location and size of shocks, expansion fans, and recirculation zone, and combustion characteristics such as flame lift-off distance. Although the effects of the pressure work on the mean flame lift-off distance are negligible, they have a significant influence on the predicted spatial fluctuations of the flame base.

LES of a lifted methanol spray flame series using the sparse Lagrangian MMC approach

Two-phase multiple mapping conditioning / large eddy simulation (MMC-LES) is applied for the first time to lifted spray flames on a vitiated coflow burner. Three flames with different inlet fuel mass loading are investigated. MMC-LES uses a hybrid Eulerian-Lagrangian-Lagrangian approach for the evolution of gas-phase flow, stochastic particles, and liquid fuel droplets, respectively. Due to the benefits of localizing mixing in a reference mixture fraction space, a sparse-Lagrangian distribution of particles is able to be used, permitting computationally efficient simulations of the flame series using gas-phase chemical kinetics that includes 32 species and 167 reactions. Heat and mass transfer between the stochastic particles and evaporative fuel droplets are also local in the reference mixture fraction space. Analysis of the gas-phase temperature fields reveals two distinct flame base stabilization phenomena. The first, which is observed for the low and intermediate fuel loading cases, produces a flat flame base spreading across the central region of the jet. The second, observed for the highest fuel loading case, produces an annular flame base in the shear layer that surrounds a cold central jet region, which is characteristic of autoignition due to entrainment of hot oxidizer from the co-flow. Except for a few axial locations, predicted radial profiles of temperature and liquid-phase velocity/size statistics yield a reasonable agreement with experimental measurements for all three flames. Furthermore, the trend of decreasing lift-off height with an increase in fuel loading is captured well.

Two-phase coupling for MMC-LES of spray combustion

A sparse-Lagrangian particle implementation of the multiple mapping conditioning / large-eddy simulation (MMC-LES) model for two-phase flows is developed with the aid of carrier-phase direct numerical simulation (CP-DNS) of a droplet-laden temporally evolving reacting double shear layer. In sparse-Lagrangian MMC for spray combustion, the liquid fuel droplets are represented by a first set of Lagrangian particles, while the reacting gas phase is described by a second set of (stochastic) particles. The two phases exchange heat and mass and a one-to-one coupling technique of liquid and gas particles with particle pair selection conditional on mixture fraction and/or temperature is introduced. The simulations show that unconditional mean and rms of mixture fraction are accurately reproduced by MMC and are largely independent of the particle coupling. Temperature, however, is significantly underpredicted when using the Eulerian mixture fraction for particle selection as is conventional for particle-particle selection in MMC. This is due to a lack of correlation between temperature and mixture fraction caused by excessive cooling of selected fluid elements due to evaporation and subsequent local flame extinction and reignition. Conditioning on temperature leads to mild improvements but does not prevent a decorrelation of the temperatures “seen” by the droplets. Alternatively, a minimization based on stochastic particle temperature is suggested. This leads to good agreement between our MMC-LES model and the CP-DNS. The comparison between the CP-DNS data and MMC-LES also confirms that the anisotropic mixing time scale derived for gaseous flows ensures an accurate degree of micro-mixing also for two-phase flows and provides very good predictions of conditional fluctuations of reacting scalars around the conditional means.

Improved MMC-LES to compute the structure of a mixed-mode turbulent flame series

An improved version of the Lagrangian multiple mapping conditioning model coupled with large eddy simulation (MMC-LES) is applied to compute the structure of a range of turbulent mixed-mode flames stabilised on the Sydney piloted burner with compositionally inhomogeneous inlet. The calculations are compared with detailed measurements. While premixed MMC-LES models are yet to be developed, the most commonly deployed version and code for MMC-LES uses a mixture-fraction-based approach and a sparse-Lagrangian notional particle method that is most suitable for non-premixed combustion. The improvements reported here are due to (i) a more rigorous density coupling approach, (ii) a more refined mixing time scale, and (iii) selective particle intensification to improve localness in physical space as well as mixture fraction space. This intensification is selectively applied in upstream regions where mixed-mode combustion dominates and is relaxed further downstream as the jet flames transition to a non-premixed flame structure. The computed results show good agreement with experimental data hence confirming the feasibility of the improved MMC-LES approach in being able to account for mixed-mode combustion as well as for finite-rate chemistry effects. These promising results warrant future extension of the selective particle intensification method to become automatically adaptive.

Mixing Time Scale Models for Multiple Mapping Conditioning with Two Reference Variables

A novel multiple mapping conditioning (MMC) approach has been developed for the modelling of turbulent premixed flames including mixture inhomogeneities due to mixture stratification or mixing with the cold surroundings. MMC requires conditioning of a mixing operator on characteristic quantities (reference variables) to ensure localness of mixing in composition space. Previous MMC used the LES-filtered reaction progress variable as reference field. Here, the reference variable space is extended by adding the LES-filtered mixture fraction effectively leading to a double conditioning of the mixing operator. The model is used to predict a turbulent stratified flame and is validated by comparison with experimental data. The introduction of the second reference variable also requires modification of the mixing time scale. Two different mixing time scale models are compared in this work. A novel anisotropic model for stratified combustion leads to somewhat higher levels of fluctuations for the passive scalar when compared with the original model but differences remain small within the flame front. The results show that both models predict flame position and flame structure with good accuracy.