Flamelet Approach Research Articles

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.

Application of computationally inexpensive CFD model in steady-state and transient simulations of pulverized sewage sludge combustion

The combustion process of pulverized fuels with high ash contents, such as sewage sludge, is significantly impacted by the amount of slag deposition in a furnace. A CFD model based on the Steady Diffusion Flamelet (SFM) approach was applied to numerically simulate the combustion of pulverized sewage sludge in a drop tube furnace. Steady-state solutions of the Reynolds-Averaged Navier–Stokes (RANS) equations already displayed good agreement with species and temperature measurements. Still, they failed to accurately predict the significant amount of ash trapped on the internal furnace surfaces (minimum deposition of 28% of the generated ash versus 5% predicted by the RANS simulations). The SFM-based CFD model’s computational efficiency enabled the conduction of large eddy simulations (LES), significantly improving the model’s predictive capabilities (27% of the generated ash deposited). Additionally, the transient simulations further improved the agreement with temperature measurement data. A novel initialization procedure was developed, which allowed the transient LES simulations to be conducted in a computationally efficient manner. The SFM-based model can effectively support research and development efforts, even for large-scale systems which require high cell counts. It provides valuable insights during the early design phases of industrial furnaces for pulverized sewage sludge combustion.

Numerical prediction of fire dynamics and the safety zone in large‐scale multiple pool fire in a dike using flamelet model

AbstractThis research aims to develop a computational fluid dynamics (CFD) methodology for estimating the safety zone around a dike with multiple pool fire (MPF). This study predicts the safety zone and burning characteristics of heptane MPF inside a square dike in calm wind and worst‐case crosswind situations using unsteady simulations. The heptane MPF is modelled using flamelet approach with large eddy simulation (LES) turbulence model incorporating the soot generation. Discrete ordinates and Moss–Brookes model estimate the effect of participating medium radiation on prediction of safety distance and soot production. The discretization is incorporated using an isotropic trimmed cell mesher with local refinement to resolve the flame characteristics in Simcenter STAR CCM+. An extensive grid‐independence study has been executed to find the optimal mesh. The flame temperature and O2 and CO2 mass fraction predictions in calm wind conditions are in good agreement with the experimental findings of Koseki and Yumoto and the maximum flame temperature predictions are within 2.8% error. The safety zone is predicted using the estimated radiative heat flux. The effect of different ordinate sets (angular discretization S4, S6, and S12) approach on safety distance prediction is investigated. The validated grid independent CFD model combined with flamelet generated manifold model and LES turbulence model is proposed to predict the safety zone for industrial MPF in crosswind scenarios, thereby preventing human fatalities and property loss.

Numerical Predictions of Soot Formation in Kerosene/Air Jet Diffusion Flame

Soot volume fraction in a turbulent diffusion flame burning kerosene/air is simulated using steady flamelet approach. The soot inception model based on the formation rate of three and two ring aromatics is used, which further accounts for inception, coagulation, surface growth, and oxidation processes. The Favre-averaged governing equations of mass, momentum, and energy are solved in conjunction with k-? turbulence model in ANSYS-FLUENT. The fairly detailed reaction mechanism for kerosene/air is coupled to the turbulent flow field by steady laminar flamelet approach, while the soot is calculated using Moss-Brookes model. The predictions are found to match well with the measurements where no significant effects are observed with the inclusion of higher order hydrocarbon as precursors and surface growth.

Computational modelling of explosions caused by failed Li‐ion batteries

AbstractThe implementation rate of renewable energy sources such as lithium‐ion batteries has grown over the last decade. Consequently, the number of explosion occurrences associated with these batteries has also increased. Such events are due to a process called thermal runaway (TR). The flamelet combustion approach has been widely used to model premixed combustion. However, its applicability for modelling accidental explosions from lithium‐ion batteries remains limited. Moreover, the effects and contributions from stress, strain, and wrinkling on the flame front in gas mixtures from Li‐ion batteries are not fully understood. As far as computational modelling is concerned, the same effects require further investigation. The current research investigates the performance of the flamelet approach for modelling premixed combustion scenarios caused by the gases ejected by a fully charged lithium‐ion‐phosphate (LFP) battery. A new laminar burning velocity correlation is proposed based on experimental data to calculate overpressure, flame position, and flame velocity in a semi‐confined geometry. Promising results are presented resorted by good agreement with experimental data.

Spray Flamelet Modeling of Turbulent Two-Phase Reacting Flows with Multi-Component Fuel in a Lean Direct Injection Combustor

ABSTRACT Towards the numerical evaluation of the performance in aero-engine combustors, implementing detailed reaction kinetics into the large eddy simulation (LES) cost-effectively is highly desirable. In this work, a newly-developed spray flamelet model is combined with a four-component jet fuel surrogate model to allow integration of the detailed kinetics in the open-source CFD code. The spray flamelet approach (SFGM) can take into account the non-adiabatic effect caused by the evaporating spray and can directly reflect the preferential evaporation, as well as multiple combustion regimes present in complex spray combustion systems. The coupling of the SFGM-LES approach is assessed by comparison with the experimental data from a Lean Direct Injection (LDI) combustor, where the real aviation kerosene, Jet-A, was utilized. The SFGM-LES approach well predicts the experimental statistics in both gas and liquid phases. It is capable of capturing the rich physics and complex flame structures, including the preferential evaporation effect and the multi-regime combustion phenomenon. The present work demonstrates that the complex nature of multi-components and the multiple-combustion regimes in the two-phase combustion can be directly included in the spray flamelet approach, and thus this model can provide new insights into the turbulent spray combustion phenomena.

A priori and a posteriori analysis of flamelet modeling for large-eddy simulations of a non-adiabatic backward-facing step

A lean premixed ethylene–air flame in a backstep configuration is simulated on multiple grids using both direct numerical simulations (DNS) with reduced order kinetic mechanism and large eddy simulations (LES) with flamelet-based thermochemistry. The configuration includes preheated reactants and a recirculation zone that provides radicals and high temperature gases to stabilize the flame. Heat losses are present due to the proximity of cooled walls. The reacting flow obtained from DNS at different resolutions is first analyzed to investigate the property of heat transfer within the recirculation region. LES based on adiabatic flamelets with a correction of the heat capacity is then tested, and its ability to account for heat losses is compared to results obtained using a three-dimensional non-adiabatic flamelet approach. Mean fields and subgrid properties are compared to those obtained from DNS to assess the capability of the LES models. The results show that the non-adiabatic flamelet approach can predict recirculation region and temperature fields with good accuracy. The model with heat capacity correction is able to effectively correct the heat capacity behavior as observed by a priori comparisons. However, in the a posteriori context, it is observed to overestimate the temperature field, although the correct size of the recirculation region is predicted. The combined a priori and a posteriori analyses on the same configuration and at different mesh resolutions allow for a precise separation of modeling effects due to heat transfer at the wall and combustion closure, thus providing indications on the LES performance in the context of flamelets.

Hybrid Unsupervised Cluster-wise Regression Approach for Representing the Flamelet Tables

A novel hybrid unsupervised cluster-wise regression approach is developed to represent the flamelet tables and speed up the computations in turbulent combustion simulations. The proposed machine learning method utilizes a cluster-wise regression technique where specialized deep neural networks are trained on different parts of the input space. A new recursive unsupervised clustering (RUC) approach is proposed that leads to a lower root-mean-square error by over 30% and improves the individual cluster’s mean absolute error by over 20%. The RUC approach enables identifying different combustion manifolds within the input space. The regression models unique to these identified manifolds accurately capture the thermo-chemical scalars for the given input data set. To balance the tradeoffs between the accuracy of flamelet table predictions and the complexities of the RUC algorithm, a hybrid model is introduced that switches between a single neural network (SNN) which is a single regression model, and the SUC RUC approaches. The hybrid unsupervised cluster-wise-regression model benefits from the lower computational costs of SNN for parts of the input space where the SNN prediction error is low and switches to the unsupervised clustering models, that is, standard (SUC) and recursive (RUC) in areas where the SNN performs poorly. The hybrid model is trained on four-dimensional steady flamelet tables and used to model methane combustion by adopting the Sandia Flame D configuration. The hybrid clustering method more accurately captures the experimental measurements of temperature, carbon monoxide (CO), and hydroxyl radical (OH) mass fraction compared to the SNN model. A new hybrid model offers significant improvements in accuracy as compared to the SNN model along with reduction of computational storage by 2 orders of magnitude compared to the original flamelet approach and reduces the total computational time in 3D reacting flow simulations.

Large Eddy Simulation of a Turbulent Dilute Ethanol Flame Using the Two-Phase Spray Flamelet Generated Manifold Approach

ABSTRACT A recently developed spray Flamelet Generated Manifolds (SFGM) approach has been extended to include turbulence–chemistry interactions for studies of turbulent spray flames based on Eulerian–Lagrangian multiphase Large Eddy Simulation (LES). The Eulerian–Eulerian two-fluid formulation of the SFGM was extended to include the mixture fraction variance to construct a 4-D manifold library. The effect of heat loss due to droplet evaporation was considered in the SFGM tabulation, and the SFGM approach was evaluated using the Sydney ethanol spray flame experimental database. The two-phase interaction was investigated from complete analyses of the continuous- and dispersed-phase dynamics. Comparisons between the numerical results and the experimental data indicate that the SFGM formulated from counterflow spray flames can produce a good agreement with the gaseous flow field and the dispersed-phase statistics. By comparing the results in terms of the temperature field with other existing models, it can be inferred that the discrepancies between the flamelet-based results and the experimental data may not depend on the choice of the flamelet approach but on the modeling of the turbulence/chemistry interaction model. A Beta-function of the normalized progress variable can be an alternative to improve the temperature predictions. Moreover, using a well-designed definition of the progress variable by finding the optimal weights of several appropriate species is another possible path to improve the predictions.

Formulation and importance of conservative transport in non-premixed flamelet models

The flamelet approach is widely used to model non-premixed turbulent combustion. In this model, chemistry is solved in mixture fraction space and the mixture fraction field is solved in physical space. Transport of reactive scalars in mixture fraction space is governed by two flow parameters: the scalar dissipation rate and the curvature of the mixture fraction field. While these two flow parameters can be easily evaluated if all scales are resolved, models are required if turbulence modeling is applied. However, conventional flow parameter models, which presume the shape of the flow parameters in mixture fraction space, do not consider that mixing in physical and mixture fraction space need to be modeled consistently, which can cause leading order errors. In this study, a consistent formulation of the governing equations and the flow parameters is derived, which is then applied within the Representative Interactive Flamelet (RIF) model to an auto-igniting, sooting, temporal n-dodecane jet under engine-relevant conditions. A Direct Numerical Simulation (DNS) is carried out and serves as reference solution for model validation. It is shown that the revised flow parameters yield superior model predictions of all investigated quantities in comparison to conventional models. Although the auto-ignition process is captured reasonably well by the conventional model, the modeling error in soot quantities is not tolerable. The revised model shows much better agreement with the DNS data and demonstrates that the RIF model is generally able to predict pollutants under the considered conditions. An analysis of the temporal soot mass evolution shows that an accurate description of both species and particle transport in mixture fraction space is essential for predicting soot formation.

Flamelet modeling of thermo-diffusively unstable hydrogen-air flames

In order to reduce CO2 emissions, hydrogen combustion has become increasingly relevant for technical applications. In this context, lean H2-air flames show promising features but, among other characteristics, they tend to exhibit thermo-diffusive instabilities. The formation of cellular structures associated with these instabilities leads to an increased flame surface area which further promotes the flame propagation speed, an important reference quantity for design, control, and safe operation of technical combustors. While many studies have addressed the physical phenomena of intrinsic flame instabilities in the past, there is also a demand to predict such flame characteristics with reduced-order models to allow computationally efficient simulations. In this work, a H2-air spherical expanding flame, which exhibits thermo-diffusive instabilities, is studied with flamelet-based modeling approaches both in a-priori and a-posteriori manner. A recently proposed Flamelet/Progress Variable (FPV) model, with a manifold based on unstretched planar flames, and a novel FPV approach, which takes into account a large curvature variation in the tabulated manifold, are compared to detailed chemistry (DC) calculations. Both flamelet approaches account for differential diffusion utilizing a coupling strategy which is based on the transport of major species instead of transporting the control variables of the manifold. First, both FPV approaches are assessed in terms of an a-priori test with the DC reference dataset. Thereafter, the a-posteriori assessment contains two parts: a linear stability analysis of perturbed planar flames and the simulation of the spherical expanding flame. Both FPV models are systematically analyzed considering global and local flame properties in comparison to the DC reference data. It is shown that the new FPV model, incorporating large curvature variations in the manifold, leads to improved predictions for the microstructure of the corrugated flame front and the formation of cellular structures, while global flame properties are reasonably well reproduced by both models.

Lagrangian filtered density function modeling of a turbulent stratified flame combined with flamelet approach

To simulate turbulent flames with high accuracy at low computational cost, Rieth et al. [“A hybrid flamelet finite-rate chemistry approach for efficient LES with a transported FDF,” Combust. Flame 199, 183–193 (2019)] have developed a hybrid method combining a combustion sub-grid model with assumed filtered density function (FDF) with a transported FDF approach. The present paper extends the hybrid approach to a stratified flame from the Cambridge stratified flame series. In contrast to the conventional Lagrangian FDF transport approach, the hybrid model applies Lagrangian particles to solve FDF transport only in selected regions, while an assumed FDF is applied in the remaining domain. With the hybrid model, the overall number of particles is strongly reduced compared to the conventional Lagrangian FDF transport model, promising great savings in computational cost. To provide a basis for the comparisons, simulations with assumed FDF or transported FDF only have also been performed. The present work aims to show the advantage of the Lagrangian transported FDF and the hybrid approach for a highly stratified flame, one of the most challenging members of the well-known Cambridge stratified flame series. Different criteria are tested for triggering the switch-over between the methods to maximize the efficiency of the hybrid approach, where basic flame quantities such as mixture fraction were predicted well with the assumed FDF model, and the temperature and mass fraction of carbon monoxide were predicted better by the hybrid method, featuring the transported FDF technique.

Simulation of a GOx-GCH4 Rocket Combustor and the Effect of the GEKO Turbulence Model Coefficients

In this study, a single injector methane-oxygen rocket combustor is numerically studied. The simulations included in this study are based on the hardware and experimental data from the Technical University of Munich. The focus is on the recently developed generalized k–ω turbulence model (GEKO) and the effect of its adjustable coefficients on the pressure and on wall heat flux profiles, which are compared with the experimental data. It was found that the coefficients of ‘jet’, ‘near-wall’, and ‘mixing’ have a major impact, whereas the opposite can be deduced about the ‘separation’ parameter Csep, which highly influences the pressure and wall heat flux distributions due to the changes in the eddy-viscosity field. The simulation results are compared with the standard k–ε model, displaying a qualitatively and quantitatively similar behavior to the GEKO model at a Csep equal to unity. The default GEKO model shows a stable performance for three oxidizer-to-fuel ratios, enhancing the reliability of its use. The simulations are conducted using two chemical kinetic mechanisms: Zhukov and Kong and the more detailed RAMEC. The influence of the combustion model is of the same order as the influence of the turbulence model. In general, the numerical results present a good or satisfactory agreement with the experiment, and both GEKO at Csep = 1 or the standard k–ε model can be recommended for usage in the CFD simulations of rocket combustion chambers, as well as the Zhukov–Kong mechanism in conjunction with the flamelet approach.

Large eddy simulation of premixed turbulent combustion using a non-adiabatic, strain-sensitive flamelet approach

In this study, a novel strained, non-adiabatic flamelet generated manifold (FGM) model is developed based on a counterflow premixed flame. The different levels of strain and heat loss are introduced into the flamelets by varying the stagnation point strain rate and burnt temperature of the counterflow configuration. The strain rate response of these flamelets is found to exhibit different extinction patterns for different ranges of burnt temperature. A priori studies are performed to compare the phase-space flame structures of the strained and unstrained flamelets. It is found that the strained flamelet degenerates towards the unstrained flamelet with burnt temperature decreasing. A bifurcation burnt temperature is further defined that separates the two types of flamelet quenching that are driven by strain and heat loss. An appropriate set of tabulation parameters is chosen that preserves the uniqueness of mapping between the manifold and the populated flamelets. The external boundaries of the tabulations are defined, where the proposed model degenerates into the conventional unstrained/non-adiabatic FGM manifold. Internal tabulation boundaries are defined to distinguish different combustion modes among stable combustion, strain-induced quenching, and heat-loss-induced quenching. The model is validated using large eddy simulation (LES) of a confined turbulent premixed jet flame. The proposed FGM model vastly increases accuracy of predictions when both strain and heat loss effects are included. Without accounting for these effects, there are discrepancies in the prediction of flame height and temperature as compared with experimental data. An analysis of the dominant physical process (strain, heat loss) that contributes to the evolution of the turbulent flame is performed.

Predicting large-scale pool fire dynamics using an unsteady flamelet- and large-eddy simulation-based model suite

A low-Mach, unstructured, large-eddy-simulation-based, unsteady flamelet approach with a generalized heat loss combustion methodology (including soot generation and consumption mechanisms) is deployed to support a large-scale, quiescent, 5-m JP-8 pool fire validation study. The quiescent pool fire validation study deploys solution sensitivity procedures, i.e., the effect of mesh and time step refinement on capturing key fire dynamics such as fingering and puffing, as mesh resolutions approach O(1) cm. A novel design-order, discrete-ordinate-method discretization methodology is established by use of an analytical thermal/participating media radiation solution on both low-order hexahedral and tetrahedral mesh topologies in addition to quadratic hexahedral elements. The coupling between heat losses and the flamelet thermochemical state is achieved by augmenting the unsteady flamelet equation set with a heat loss source term. Soot and radiation source terms are determined using flamelet approaches for the full range of heat losses experienced in fire applications including radiative extinction. The proposed modeling and simulation paradigm are validated using pool surface radiative heat flux, maximum centerline temperature location, and puffing frequency data, all of which are predicted within 10% accuracy. Simulations demonstrate that under-resolved meshes predict an overly conservative radiative heat flux magnitude with improved comparisons as compared to a previously deployed hybrid Reynolds-averaged Navier–Stokes/eddy dissipation concept-based methodology.

Experimental and numerical study of water sprayed turbulent combustion: Proposal of a neural network modeling for five-dimensional flamelet approach

Owing to the increasing worldwide demand for natural gas, the development of a large submerged combustion vaporizer is required. Its burner is equipped with a water spray nozzle to reduce nitrogen oxides, and a practical simulation method is required for the optimal design. The non-adiabatic flamelet approach can predict the combustion emissions and is useful for reducing simulation costs. However, as the number of control variables increases, the database requires larger memory and cannot be dealt with by general computers. In this study, an artificial neural network (ANN) model based on a five-dimensional flamelet database, which includes the effects of heat loss and vapor concentration by sprayed water evaporation, is developed. Furthermore, large eddy simulations (LESs) for turbulent combustion fields with and without water spray are conducted employing flamelet generated manifold (FGM) approach with this ANN model, and the validity is investigated. For comparison, a lab-scale burner equipped with a water spray nozzle is manufactured, and combustion experiments with and without water spray are conducted. The results show that CO, NO, temperature, and reaction rate of progress variable predicted by the present ANN model are in good agreement with those of a five-dimensional flamelet database. In the condition without water spray, the flame behavior predicted by the LES employing the FGM/ANN approach is in good agreement with that employing the conventional FGM approach, while indicating much lower memory, although there appeared some quantitative discrepancies in the temperature against the experiment probably partially because of the insufficiency of the FGM approach for the present complex flame structure. In the condition with water spray, the LES employing the FGM/ANN approach is able to capture the effect of the water spray on the flame behavior in the experiment, such that the water spray decreases the temperature, which causes the decrease in NO but increase in CO.

Large eddy simulation of two-phase reacting turbulent flow in a pilot-scale pulverized coal combustion furnace with flamelet model

A three-dimensional numerical simulation was performed to investigate the physics and combustion characteristics of a two-phase reacting turbulent flow in a pilot-scale pulverized coal combustion furnace. This included an elementary reaction mechanism using an extended flamelet/progress variable (EFPV) method. The simulation was validated via comparison with an experiment in terms of the gaseous temperature and distribution of the gas mole fraction. The EFPV method predicted the flame structure and combustion characteristics of the pulverized coal. In the main reaction zone where the released gas combustion was dominant, two separate combustion regions were observed, and they were attributed to hydrocarbons and CO combustion. Gas flow characteristics such as mixing of low temperature gas and hot burnt gas were well described in the inner recirculation zone. The CO2 conversion reaction to CO occurred slowly and decreased the gaseous temperature beyond the main reaction zone in the low and zero oxygen environments. The simulation predicted the unburned CO combustion correctly beyond the flame when staged air was injected; however, the combustion rate was overestimated due to the fundamental assumption of the EFPV method, attributable to the limitations of the steady state flamelet approach.

Assessment of a flamelet approach to evaluating mean species mass fractions in moderately and highly turbulent premixed flames

Complex-chemistry direct numerical simulation (DNS) data obtained from lean methane-air turbulent flames are analyzed to perform a priori assessment of predictive capabilities of the flamelet approach to evaluating mean concentrations of various species in turbulent flames characterized by Karlovitz numbers Ka=6.0, 74.0, and 540. Six definitions of a combustion progress variable c are probed and two types of probability density functions (PDFs) are adapted: (i) actual PDFs extracted directly from the DNS data or (ii) presumed β-function PDFs obtained using the DNS data on the first two moments of the c-field. Results show that the mean density, the mean temperature, and the mean mass fractions of CH4, O2, H2O, CO2, CO, CH2O, CH3, and HCO are very well predicted using the temperature-based combustion progress variable cT and the actual PDF. For other considered species, the quantitative predictions are worse but still appear to be encouraging (with the exception of CH3O at Ka=540). The use of the flamelet library obtained from the equidiffusive laminar flame improves results for H2, HO2, and H2O2 at the highest Karlovitz number. Alternative definitions of the combustion progress variable perform worse and the reasons for this are explored. The use of the β-function PDF yields worse results for intermediate species such as OH, O, H, CH3, and HCO, with this PDF being significantly different from the actual PDF. Application of the flamelet approach to rates of production/consumption of various species is also addressed and implications of obtained results for modeling are discussed.

Unsteady flamelet modeling for N[formula omitted]H[formula omitted]/N[formula omitted]O[formula omitted] flame accompanied by hypergolic ignition and thermal decomposition

In this study, the applicability of the flamelet approach to numerical simulations of hydrazine (N2H4)/nitrogen tetroxide (NTO, N2O4) combustion, in which hypergolic ignition and thermal decomposition occur, is investigated in terms of two-dimensional numerical simulations of two types of N2H4/NTO jet flames, namely, the gaseous N2H4/NTO jet flame and the N2H4 spray jet flame in the gaseous NTO stream. In case of the gaseous jet flame, the numerical simulation is performed employing the unsteady flamelet/progress variable (UFPV) approach. In case of the spray jet flame, on the other hand, a non-adiabatic unsteady flamelet/progress variable (NAUFPV) approach, which combines the UFPV approach and the non-adiabatic flamelet/progress variable (NAFPV) approach, is proposed. The validity of these and some other existing flamelet approaches is investigated by comparison with the results obtained using the exact approach, in which detailed chemical reactions are directly solved. The results show that the UFPV and NAUFPV approaches drastically improve predictions of the N2H4/NTO gaseous and spray combustion behavior, respectively, including the ignition process, the flame lift-off height, and the distributions of temperature and chemical species concentrations. This indicates that self-decomposition flame of fuel is successfully captured by the UFPV approach, and that the NAUFPV approach can additionally take into account the heat loss effect due to evaporation of droplets.

A universal interface model for diffusion dominant combustion flame by coupling phase field approach and level-set equation

A unified mathematical formulation of fluid interface is derived by phase field and level-set approaches and conservation law of thermodynamic variable. In this work, it is applied for a multi-color flamelet approach model of combustion flows which may be coupled to a steep gradient of thermodynamic condition such as a diffusion of fuel mixture profile in the flame thickness. Its applications to large eddy simulation of turbulent and compressible combustion flows are discussed, too.