Multiple Mapping Conditioning Approach 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.

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.

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.

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.

Sparse-Lagrangian PDF Modelling of Silica Synthesis from Silane Jets in Vitiated Co-flows with Varying Inflow Conditions

This paper presents a comparison of experimental and numerical results for a series of turbulent reacting jets where silica nanoparticles are formed and grow due to surface growth and agglomeration. We use large-eddy simulation coupled with a multiple mapping conditioning approach for the solution of the transport equation for the joint probability density function of scalar composition and particulate size distribution. The model considers inception based on finite-rate chemistry, volumetric surface growth and agglomeration. The sub-models adopted for these particulate processes are the standard ones used by the community. Validation follows the “paradigm shift” approach where elastic light scattering signals (that depend on particulate number and size), OH- and SiO-LIF signals are computed from the simulation results and compared with “raw signals” from laser diagnostics. The sensitivity towards variable boundary conditions such as co-flow temperature, Reynolds number and precursor doping of the jet is investigated. Agreement between simulation and experiments is very good for a reference case which is used to calibrate the signals. While keeping the model parameters constant, the sensitivity of the particulate size distribution on co-flow temperature is predicted satisfactorily upstream although quantitative differences with the data exist downstream for the lowest coflow temperature case that is considered. When the precursor concentration is varied, the model predicts the correct direction of the change in signal but notable qualitative and quantitative differences with the data are observed. In particular, the measured signals show a highly non-linear variation while the predictions exhibit a square dependence on precursor doping at best. So, while the results for the reference case appear to be very good, shortcomings in the standard submodels are revealed through variation of the boundary conditions. This demonstrates the importance of testing complex nanoparticle synthesis models on a flame series to ensure that the physical trends are correctly accounted for.

Numerical investigation of flow and scalar fields of piloted, partially-premixed dimethyl ether/air jet flames using stochastic multiple mapping conditioning approach

Turbulent piloted partially-premixed jet flames of dimethyl ether/air have been investigated using the Reynolds-Averaged Navier-Stokes (RANS) based stochastic multiple mapping conditioning (MMC) approach. The MMC model combines the advantages of mapping closure concept, conditional moment closure, and probability density function (PDF) methods. In the present work, the evolution of the mapping function in the reference space is described using a single reference variable based on the mixture fraction. To achieve localness in the composition space, the turbulent mixing is conditioned on the reference space. In addition to localness, MMC preserves the various characteristics of a good mixing model, such as linearity, Gaussianity, independence, and boundedness. A skeletal chemical mechanism for dimethyl ether is used, which consists of 28 species and 24 reversible reactions. Modified Curl's mixing model is adapted to model the micro-mixing term, and standard two-equation k−ε turbulence model is used to model the Reynolds stress term with a modified set of constants. The computed conditional and unconditional statistics demonstrate an excellent agreement with the available experimental data even for flame displaying a large degree of local extinction and re-ignition. For these flames, radical species distribution conditioned on mixture fraction confirms the physical separation between the OH and CH2O species, which was earlier reported using simultaneous laser-induced fluorescence measurements of these radicals. Predicted unconditional scalar dissipation rate for DME-D and DME-F flames reaffirm that near the inlet an overlap between OH and CH2O radicals are observed where the scalar dissipation rate is fairly high. Subsequently, a distinct separation between these radicals becomes evident at downstream locations where the scalar dissipation rate decreases. For the flames investigated here, a strong correlation is noticed between the peak heat release rate and the reaction rate indicator, ROH based on the product of concentrations of OH and CH2O radicals.

Numerical investigation of auto-igniting turbulent lifted CH4/air jet diffusion flames in a vitiated co-flow using a RANS based stochastic multiple mapping conditioning approach

Numerical simulations of auto-igniting turbulent lifted jet diffusion flames of CH4/air fuel issued into a vitiated coflow of lean combustion products of H2/air are performed using Reynolds-averaged Navier-Stokes (RANS) based stochastic multiple mapping conditioning (MMC) approach. A two-dimensional axisymmetric formulation is used to model the fluid flow, where the gas-phase turbulence terms are closed using the standard two-equation k-ε turbulence model with a modified set of constants. A reduced chemical mechanism ARM2 is used which consists of 19 species and 15 reactions derived from the GRI 3.0 mechanism. In MMC, the concept of mapping function is used, which approximates the cumulative probability distribution of the major scalar, namely mixture fraction for nonpremixed combustion. The corresponding variance of the major scalar is modelled by choosing a standard implementation of the major mixing time scale τϕ modelled in terms of the turbulent time scale as τϕ=τt/Cϕ. For all simulations reported herein, the same major mixing time constant Cϕ=3.0 is used. Additionally, in MMC, a minor mixing time scale τmin is introduced which controls fluctuations of scalars relative to the major fluctuations via the minor mixing time constant, Cmin. Three different values of Cmin=(τmin/τϕ)=0.25,0.35and0.50 are used and the corresponding ratios of minor to turbulent time scales are τmin/τt=0.083,0.116 and 0.166, respectively. The conditional and unconditional reactive scalar fields are found to be highly dependent on the choice of Cmin and hence the ratio of the minor and major mixing time scales. The numerical results are thoroughly validated against the experimental measurements. The variation in lift-off height is found to be in good agreement with the experimental data for the entire range of coflow temperature for Cmin=0.25. Also, the predicted conditional and unconditional scalar fields from the present RANS-MMC model shows an excellent agreement with the experimental measurements.

Numerical modeling of turbulent premixed combustion using RANS based stochastic multiple mapping conditioning approach

Stochastic multiple mapping conditioning (MMC) approach has been used to model a turbulent lean premixed jet flame of methane/air mixture within the Reynolds averaged Navier Stokes (RANS) framework. In MMC, the reaction progress variable is used as the reference variable. The mapping function approximates the cumulative probability distribution of reaction progress variable and the corresponding variance can be controlled by a standard implementation of the scalar mixing timescale. A separate equation is being solved for the evolution of the mapping function. Modified Curl's mixing model has been implemented to model the micro-mixing term. The stochastic MMC solver has been fully integrated with the RANS flow solver. Turbulence has been modeled using two equation k−ɛ model with a modified set of constants. A skeletal mechanism of 19 species and 15 reactions based on GRI 3.0 has been used in the present simulations. The Sydney piloted premixed jet burner (PPJB) operating in the distributed combustion regime has been considered for the model validation. Computed radial profiles of the mean axial velocity and species mass fractions are found to be in very good agreement with the available experimental data. In some instances, the RANS-MMC model produces a better match with the experimental data compared to the results obtained from other state-of-the-art turbulent combustion models.

Numerical simulations of turbulent lifted jet diffusion flames in a vitiated coflow using the stochastic multiple mapping conditioning approach

Lifted turbulent jet diffusion flames of H2/N2 issued into a hot coflowing stream of combustion products from a lean premixed H2/air mixture are simulated using the stochastic multiple mapping conditioning (MMC) approach within the Reynolds-averaged Navier–Stokes (RANS) framework. The underlying turbulent flow is modeled using the two-equation k–ɛ model with modified constants. In the MMC approach, large-scale turbulent fluctuations are emulated by introducing suitable reference variables. A single reference variable is used here to describe the evolution of mixture fraction via a mapping function. The modified Curl's model has been adapted to model the micro-mixing term. A detailed chemical kinetic mechanism involving 9 species and 21 reversible reactions is used for H2/O2 combustion. The computed results from the present simulations are found to be in excellent agreement with the available experimental data. Numerical results are found to be sensitive to change in the minor dissipation timescale, which certainly controls the conditional fluctuations around the conditional mean. Also, the predicted flame lift-off heights obtained using the minor mixing time constant Cmin = 0.25 are found to be in close proximity with the experimentally observed values for the entire range of coflow temperatures.

A direct approach to generalised multiple mapping conditioning for selected turbulent diffusion flame cases

This work presents a direct and transparent interpretation of two concepts for modelling turbulent combustion: generalised Multiple Mapping Conditioning (MMC) and sparse-Lagrangian Large Eddy Simulation (LES). The MMC approach is presented as a hybrid between the Probability Density Function (PDF) method and approaches based on conditioning (e.g. Conditional Moment Closure, flamelet, etc.). The sparse-Lagrangian approach, which allows for a dramatic reduction of computational cost, is viewed as an alternative interpretation of the Filtered Density Function (FDF) methods. This work presents simulations of several turbulent diffusion flame cases and discusses the universality of the localness parameter between these cases and the universality of sparse-Lagrangian FDF methods with MMC.

A Generalised Multiple Mapping Conditioning Approach for Turbulent Combustion

This paper follows the evolution in understanding of the multiple mapping conditioning (MMC) approach for turbulent combustion and reviews different implementations of MMC models. As the MMC name suggests, the original version represents a consistent combination of CMC-type conditional equations (conditional moment closure) and generalised mapping closure. It seems that the strength of the MMC model, and especially that of its stochastic version, lies in a more general (and much more transparent) interpretation. In this new generalised interpretation, we can replace complicated derivations by physical reasoning and the model appears to be a natural extension of modelling approaches developed in recent decades. MMC can be seen as a methodology for enforcing certain known characteristics of turbulence on a conventional mixing model. This is achieved by localising the mixing operation in a reference space. The reference space variables are selected to emulate the properties of a turbulent flow which have a strong effect on reactive quantities. The best and simplest example is an MMC model which has a single reference variable emulating the mixture fraction. In diffusion flames turbulent fluctuations of reacting quantities are strongly correlated with fluctuations of the mixture fraction. By making mixing local in the reference mixture fraction space a CMC-type mixing closure is enforced. In the original interpretation of MMC the reference variables are modelled as Markov processes. Since the reference variables should emulate properties of turbulent flows as realistically as possible the next step, and the basis of generalised MMC, is to remove the Markovian restriction and set reference variables equal to traced Lagrangian quantities within DNS or LES flow fields. Indeed, no Markov value can emulate the mixture fraction better than the mixture fraction itself. (Using a Markov vector process of dimension higher than the number of conditioning variables represents a more economical alternative for producing reference variables in generalised MMC.) The generalised MMC approach effectively incorporates the mixture fraction-based models, the PDF methods and LES/DNS techniques into a single methodology with possibility of blending useful features developed previously for conventional models. The generalised approach to MMC stimulates a more flexible understanding of simulations using sparsely placed Lagrangian particles as tools that may provide accurate joint distributions of reactive scalars at relatively low computational cost. The physical reasoning behind the new interpretation of MMC is supported by example computations for a partially premixed methane/air diffusion flame (Sandia Flame D). The scheme utilises LES for the dynamic field and a sparse-Lagrangian filtered density function method with MMC mixing for the scalar field. Two different particle mixing schemes are tested. Simulations are performed using only 35,000 Lagrangian particles (of these only 10,000 are chemically active) on a single workstation. The relatively low computational cost allows the use of realistic chemical kinetics containing 34 reactive species and 219 reactions.