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A Generalized Langevin Model (GLM) formulation to be used in transported joint velocity-scalar probability density function methods is recalled in order to imply a turbulent scalar-flux model where the pressure-scrambling term is in correspondence with standard Monin's return-to-isotropy term. The proposed non-constant C0 formulation is extended to seen-velocity models for particle dispersion modeling in dispersed two-phase flows. This allows us to correct the wrong turbulent scalar-flux modeling in the limit of tracer particles. Moreover, this allows us to have a more general formulation in order to consider advanced Reynolds-stress models. The cubic model of Fu, Launder, and Tselepidakis is considered, together with the model of Merci and Dick for turbulent dissipation. Results are presented for different swirling and recirculating single-phase and two-phase flows, showing the capabilities of the proposed non-constant C0 GLM formulations compared to the standard GLM.

Neglecting the effect of thermal diffusion (Soret effect), we consider different formulations of multicomponent diffusion as proposed by Arias-Zugasti et al. (2016), for mixtures of dilute gases with large numbers of components. In particular, we detail the practical implementation of Model 1 + M (loc.cit.) using the lowest order approximation. This is a simple and easy to implement approach, where the 1 + M main species can be chosen locally (see the example provided as supplementary material). These new formulations of multicomponent diffusion are compared to the formulation of Dixon-Lewis, used for instance in the Chemkin package, and also to the widely used mixture-averaged simplification. Steady flamelets are first considered for very different fuels (hydrogen, methane or dodecane) in order to show some differences and limitations of the different formulations, and in order to compare computational costs when different numbers of species are involved. An unsteady auto-igniting counterflow diffusion flamelet of methane in a coflow of hot products is also considered. In this way, unsteady 1D calculations can be performed, still including all the challenges of multicomponent diffusion transport as would appear for instance in Direct Numerical Simulations (DNS) of turbulent flames. The different comparisons in terms of precision and cost show that Model 1 + M truncated to the lowest order can be more efficient than the mixture-averaged approach, while reproducing the results of Dixon-Lewis multicomponent diffusion. The efficiency of the proposed approach is mainly due to the evaluation of fewer binary diffusion coefficients, therefore reducing significantly the number of time-consuming operations. Finally, we show that the definition of 1 + M main species can also be used to simplify the time-consuming evaluation of the mixture viscosity, leading to an important further reduction of CPU time that makes the lowest order Model 1 + M always more efficient than the mixture-averaged formulation.

[EN] Engine fuel spray modeling still remains a challenge, especially in the dense near-nozzle region. This region is difficult to experimentally access and also to model due to the complex and rapid liquid and gas interaction. Modeling approaches based on Lagrangian particle tracking have failed in this area, while Eulerian modeling has proven to be particularly useful. Interface resolved methods are still limited to primary atomization academic configurations due to excessive computational requirements. To overcome those limitations, the single-fluid diffuse interface model known as Sigma-Y, arises as a single-framework for spray simulations. Under the assumption of scale separation at high Reynolds and Weber numbers, liquid dispersion is modeled as turbulent mixing of a variable density flow. The concept of surface area density is used for representing liquid structures, regardless of the complexity of the interface. In this work, a LES based implementation of the Sigma-Y model in the OpenFOAM CFD library is applied to simulate the ECN Spray A configuration. Model assessment is performed for both near- and far-field spray development regions using different experimental diagnostics available from ECN database. The CFD model is able to capture near-nozzle fuel mass distribution and, after Sigma equation constant calibration, interfacial surface area. Accurate predictions of spray far-field evolution in terms of liquid and vapor tip penetration and local velocity can be simultaneously achieved. Model accuracy is lower when compared to mixture fraction axial evolution, despite radial distribution profiles are well captured., This work was partially funded by the Spanish Ministerio de Economia y Competitividad within the frame of the CHEST (TRA2017-89139-C2-1-R) project. The computations were partially performed on the Tirant III cluster of the Servei d'Informatica of the University of Valencia (vlc38-FI-2018-2-0006). Authors acknowledge the computer resources at Picasso and the technical support provided by Universidad de Malaga (UMA) (RES-FI-2018-1-0039).

[EN] Diesel spray modelling still remains a challenge, especially in the dense near-nozzle region. This region is difficult to experimentally access and also to model due to the complex and rapid liquid and gas interaction. Modelling approaches based on Lagrangian particle tracking have struggled in this area, while Eulerian modelling has proven particularly useful. An interesting approach is the single-fluid diffuse interface model known as Σ-Y, based on scale separation assumptions at high Reynolds and Weber numbers. Liquid dispersion is modelled as turbulent mixing of a variable density flow. The concept of surface area density is used for representing liquid structures, regardless of the complexity of the interface. In this work, an implementation of the Σ-Y model in the OpenFOAM CFD library is applied to simulate the ECN Spray A in the near nozzle region, using both RANS and LES turbulence modelling. Assessment is performed with measurements conducted at the Advanced Photon Source at Argonne National Laboratory (ANL). The ultra-smallangle x-ray scattering (USAXS) technique has been used to measure the interfacial surface area, and x-ray radiography to measure the fuel dispersion, allowing a direct evaluation of the Σ-Y model predictions., Authors acknowledge that part of this work was partially funded by the Spanish Ministry of Economy and Competitiveness in the frame of the COMEFF (TRA2014-59483-R) project. Parts of this research were performed at the 7-BM and 9-ID beam lines of the Advanced Photon Source at Argonne National Laboratory. Use of the APS is supported by the U.S. Department of Energy (DOE) under Contract No. DEAC02-06CH11357. The research was partially funded by DOE's Vehicle Technologies Program, Office of Energy Efficiency and Renewable Energy. The authors would like to thank Team Leaders Gurpreet Singh and Leo Breton for their support of this work

A transported probability density function (PDF) method developed for pulverized coal combustion is applied in simulations of a semi-industrial scale furnace. It is found that the simulation results are sensitive to the chosen model for unclosed terms in the gas-phase PDF transport equation due to the mass transfer from the solid to the gas phase through devolatilization and char combustion. A model which leads to a generation of mixture fraction fluctuations provides results which are in close agreement with the measurements. Two different models for the gas phase composition seen by the coal particles are investigated. One model is based on the local mean values of the gas composition and one model provides time correlated fluctuations of the seen composition. Small differences between the two model results are observed in the predictions of the char burnout. The simulation results are further used to analyze commonly adopted model assumptions in presumed PDF methods. It is found that both, the char combustion mixture fraction and the enthalpy are not statistically independent from the volatile mixture fraction. It is further shown that the marginal PDF of the volatile mixture fraction is not well approximated by a beta function PDF in regions of rapid devolatilization. The marginal enthalpy PDF indicates significant enthalpy fluctuations which are usually neglected in presumed PDF methods.

A transported probability density function (PDF) method is developed for pulverized coal combustion. Two separate PDF transport equations, one for the gas phase (joint velocity-composition PDF) and one for the coal particle phase, are solved by means of stochastic Lagrangian methods. The gas composition is described by two mixture fractions (one that tracks the devolatilization products and one that tracks the char combustion products) and the total specific enthalpy. Two different models are proposed for the unclosed terms in the gas-phase PDF transport equation due to the mass transfer from the solid to the gas phase through devolatilization and char combustion. To close the transport equation for the coal particle PDF, the gas phase velocity and composition sampled along the coal particle trajectories are modeled. Radiative heat transfer is modeled by a discrete transfer method (DTM) to solve for the Reynolds averaged radiative heat transfer equation for a gray absorbing emitting and scattering gas–particle mixture. The turbulence–radiation interaction of the emission is given in closed form in the proposed two-phase PDF approach.

The modeling of a reacting swirling flow behind a bluff-body burner (SM1) in the framework of RANS and transported scalar PDF is presented. The EMST mixing model is applied and the composition space is reduced to mixture fraction ( Z ) and a progress variable (CO 2 mass fraction, Y CO 2 ) by means of a Reaction Diffusion Manifold (REDIM). With an ad hoc adjustment of the turbulent Schmidt number, the mean flow and mixing fields obtained are comparable to LES results from the literature. The REDIM reduction of the composition space to ( Z , Y CO 2 ) is discussed and its validity for the present swirling flame is first considered by an a priori comparison with experimental data. The ( Z , Y CO 2 ) – scatter plots from the transported PDF calculation show the capacity to reproduce the mixing between fresh air and hot products in the recirculation zone above the bluff-body. However, too little scatter is observed. The study of tracer trajectories helps to better understand the capacities and limitations of the modeling approach. Zones where mixing competes with reaction can be identified, and coincide with the highly rotating collar region where local extinction is expected to take place. However, in our modeling, the competition between mixing and reaction is not enough to lead to local extinction. An important modeling deficiency is claimed to be the use of a mean time scale in the EMST mixing model, which limits the possibilities to model high scalar dissipation rate events.

A computational study has been made of bluff-body stabilized turbulent jet flames with strong turbulence-chemistry interaction (Sydney Flames HM1 and HM3). The wide range of scales in the problem is described using a combination of a standard second moment turbulence closure, a joint scalar transported probability density function (PDF) method and the Reaction-Diffusion Manifold (REDIM) technique. The latter provides a reduction of a detailed chemistry mechanism, taking into account effects of laminar diffusion. In an a priori test it is evaluated to what extent the single shot experimental data are located on the reaction-diffusion manifold. Next, computed spatial profiles of mean and variance of independent and dependent scalar variables and profiles of conditional averages and variances (conditional on mixture fraction) are compared to the experimental results. The quality of these predictions is interpreted in relation to the a priori analysis. In general, simulations using the REDIM approach for reduction of detailed C2-chemistry confirm earlier findings for micro-mixing model behavior, obtained with a skeletal Cl-mechanism. Nevertheless it is concluded that the experiments show important features that are not described by the currently used REDIM.

Numerical simulation results are presented for three turbulent jet diffusion flames, stabilized behind a bluff body (Sydney Flames HM1-3). Interaction between turbulence and combustion is modeled with the transported joint-scalar PDF approach. The focus of the study is on the impact of the quality of simulation results in physical space on the behavior of two micro-mixing models in composition space: the Euclidean Minimum Spanning Tree (‘EMST’) model and the modified Curl coalescence dispersion (‘CD’) model. Profiles of conditional means and variances of thermo-chemical quantities, conditioned on the mixture fraction, are discussed in the recirculation region and in the neck zone behind. The impact of the flow and mixing fields in physical space on the mixing model behavior in composition space is strong for the CD model and increases as the turbulence – chemistry interaction becomes stronger. The EMST conditional profiles, on the contrary, are hardly affected.

A comparative study is presented of the impact of chemistry modeling on the behavior of 2 micro-mixing models in transported scalar PDF simulations of turbulent non-premixed flames. The micro-mixing models are CD (modified Curl's Coalescence/Dispersion) and EMST (Euclidean Minimum Spanning Tree). A first order non-linear k-e turbulence model is applied for the turbulent flow and mixing fields. Three C1 chemistry models are considered: 2 skeletal schemes containing 16 species and 31, resp. 41 elementary reactions, and one augmented reaction scheme (ARM), consisting of 9 independent species and 5 global reaction steps. The test cases considered are the piloted turbulent Delft Flame III jet diffusion flame and the bluff-body stabilized turbulent non-premixed Sydney HM1 flame. With EMST the chemistry model choice has a negligible effect on the micro-mixing model behavior or on the results in physical space. With CD on the other hand, larger differences appear.

An unsteady flamelet/progress variable (UFPV) approach is used to model a lifted H2/N2 flame in a RANS framework together with presumed PDF. We solve the unsteady flamelets both in physical space and in mixture fraction space. We show that in the former case, the scalar dissipation rate profile strongly varies in time (while it is assumed to be fixed in time in the latter). However, this does not result in significant qualitative differences in the corresponding flamelet libraries. The progress variable is carefully defined, including both the main combustion product (H2O) and a key radical species in ignition process (HO2). The presumed-PDF model is proposed in terms of the non-normalised progress variable, without assuming its statistical independence with mixture fraction. We introduce a modelled transport equation for the mean progress variable which is consistent with the basic underlying UFPV assumption, derived from the Lagrangian flamelet model. The influence of different model parameters on the results for the mean temperature and mean species mass fractions and their fluctuations is discussed. Good results are obtained for the conditions of the considered lifted flame where detailed experimental data is available. However, at low coflow temperature the modelled flame lift-off height is shorter than expected., This work is supported by the Comunidad de Madrid through Project HYSYCOMB P2009/ENE-1597 and by the Spanish Ministry of Economy and Competitiveness under Projects ENE2008-06515-004-02 and CSD2010-00011. This research was also partially supported by the Generalitat Valenciana inside the program Ajudes per a la realitzacio de projectes d'I+D per a grups de investigaclel emergent (Reference GV/2013/041), which is gratefully acknowledged.

Numerical simulation results are presented for the turbulent piloted jet diffusion flame ‘Delft Flame III’. In this flame, which is one of the target flames of the International Workshop on Measurements and Computations of Turbulent Nonpremixed Flames (TNF), effects of turbulence-chemistry interaction are strong and modelling the turbulence-chemistry interaction is a challenge. After an outline of the theoretical framework, a comparison is presented of results with on the one hand the velocity-scalar transported probability density function (PDF) approach with reduced chemistry (ILDM) and on the other hand the scalar PDF approach with detailed chemistry (C 1 -mechanism). The same micromixing model (modified coalescence-dispersion model, CD) is used in both studies. The reasons for the significantly better prediction of the mean temperature field by the scalar PDF calculations are discussed. Results of other micromixing models are briefly mentioned. To cite this article: D. Roekaerts et al., C. R. Mecanique 334 (2006).

Numerical simulation results are presented for turbulent jet diffusion flames with various levels of turbulence–chemistry interaction, stabilized behind a bluff body (Sydney Flames HM1–3). Interaction between turbulence and combustion is modeled with the transported joint-scalar PDF approach. The mass density function transport equation is solved in a Lagrangian manner. A second-moment-closure turbulence model is applied to obtain accurate mean flow and turbulent mixing fields. The behavior of two micromixing models is discussed: the Euclidean minimum spanning tree model and the modified Curl coalescence dispersion model. The impact of the micromixing model choice on the results in physical space is small, although some influence becomes visible as the amount of local extinction increases. Scatter plots and profiles of conditional means and variances of thermochemical quantities, conditioned on the mixture fraction, are discussed both within and downstream of the recirculation region. A distinction is made between local extinction and incomplete combustion, based on the CO species mass fraction. The differences in qualitative behavior between the micromixing models are explained and quantitative comparison to experimental data is made.

Numerical simulation results are presented for a turbulent nonpremixed flame with local extinction and reignition. The transported scalar PDF approach is applied to the turbulence–chemistry interaction. The turbulent flow field is obtained with a nonlinear two-equation turbulence model. A C1 skeletal scheme is used as the chemistry model. The performance of three micromixing models is compared: the interaction by exchange with the mean model (IEM), the modified Curl's coalescence/dispersion model (CD) and the Euclidean minimum spanning tree model (EMST). With the IEM model, global extinction occurs. With the standard value of model constant C ϕ = 2 , the CD model yields a lifted flame, unlike the experiments, while with the EMST model the correct flame shape is obtained. However, the conditional variances of the thermochemical quantities are underestimated with the EMST model, due to a lack of local extinction in the simulations. With the CD model, the flame becomes attached when either the value of C ϕ is increased to 3 or the pilot flame thermal power is increased by a factor of 1.5. With increased value of C ϕ better results for mixture fraction variance are obtained with both the CD and the EMST model. Lowering the value of C ϕ leads to better predictions for mean temperature with EMST, but at the cost of stronger overprediction of mixture fraction variance. These trends are explained as a consequence of variance production by macroscopic inhomogeneity and the specific properties of the micromixing models. Local time stepping is applied so that convergence is obtained more quickly. Iteration averaging reduces statistical error so that the limited number of 50 particles per cell is sufficient to obtain accurate results.

A bluff-body stabilized nonpremixed flame and the corresponding nonreacting flow were investigated. Several differential Reynolds-stress models (DRSM) were used. The transport equations for mean mixture fraction, variance of mixture fraction and Reynolds flux of mixture fraction were also solved. It was found that the performance of the reynolds-stress models was different in the nonreacting flow and the reacting flow., In the initial phase of this work B. Naud was Ph.D. student at the Thermal and Fluids Sciences Section, TU Delft, supported by the Foundation for Fundamental Research on Matter (FOM) and Guoxiu Li was having a sabbatical leave at TU Delft, supported by a research fellowship from Delft University of Technology

Steady 2D axisymmetric RANS and hybrid RANS/PDF calculations are performed to predict the turbulent flow and mixing fields of a swirling bluff body stabilized flame ('SM1'), studied experimentally at Sydney University and Sandia National Laboratories. Turbulence is modeled with a non-linear k-epsilon type model, taking into account effects of rotation and streamline curvature on turbulence. Flow field predictions are in reasonable agreement with experimental data. However, the agreement for mean mixture fraction and mixture fraction variance with experimental results is less satisfactory. The influence of the chemistry model, i.e. the use of a single laminar flamelet or the REDIM approach, is studied in transported PDF calculations with the EMST micro-mixing model. The amount of scatter is limited and observed differences are small. The combination REDIM/EMST does not reproduce the local extinction seen in the experiments. The direct comparison with the coalescence/dispersion (CD) mixing model could not be done with the same model parameter settings, as the flame extinguishes when using the REDIM approach together with the CD mixing model. Therefore, a final calculation with CD is performed with an increased value C-phi=3 and a steady solution is found. There is more scatter than with EMST, resulting in lower values for temperature and Y(CO2). Still, with the combination REDIM/CD, the level of local extinction is still under-estimated.

Two transported PDF strategies, joint velocity-scalar PDF (JVSPDF) and joint scalar PDF (JSPDF), are investigated for bluff-body stabilized jet-type turbulent diffusion flames with a variable degree of turbulence–chemistry interaction. Chemistry is modeled by means of the novel reaction-diffusion manifold (REDIM) technique. A detailed chemistry mechanism is reduced, including diffusion effects, with N 2 and CO 2 mass fractions as reduced coordinates. The second-moment closure RANS turbulence model and the modified Curl’s micro-mixing model are not varied. Radiative heat loss effects are ignored. The results for mean velocity and velocity fluctuations in physical space are very similar for both PDF methods. They agree well with experimental data up to the neck zone. Each of the two PDF approaches implies a different closure for the velocity-scalar correlation. This leads to differences in the radial profiles in physical space of mean scalars and mixture fraction variance, due to different scalar flux modeling. Differences are visible in mean mixture fraction and mean temperature, as well as in mixture fraction variance. In principle, the JVSPDF simulations can be closer to physical reality, as a differential model is implied for the scalar fluxes, whereas the gradient diffusion hypothesis is implied in JSPDF simulations. Yet, in JSPDF simulations, turbulent diffusion can be tuned by means of the turbulent Schmidt number. In the neck zone, where the turbulent flow field results deteriorate, the joint scalar PDF results are in somewhat better agreement with experimental data, for the test cases considered. In composition space, where results are reported as scatter plots, differences between the two PDF strategies are small in the calculations at hand, with a little more local extinction in the joint scalar PDF results.

Numerical simulation results are presented for 'Delft Flame III', a piloted jet diffusion flame with strong turbulence-chemistry interaction. While pilot flames emerge from 12 separate holes in the experiments, the simulations are performed on a rectangular grid, under the assumption of axisymmetry. In the first part of the paper, flow and mixing field results are presented with a non-linear first order k-ε model, with the transport equation for ε based on a modeled enstrophy transport equation, for cold and reactive flows. For the latter, the turbulence model is applied in combination with pre-assumed β-PDF modeling for the turbulence-chemistry interaction. The mixture fraction serves as conserved scalar. Two chemistry models are considered: chemical equilibrium and a steady laminar flamelet model. The importance of the turbulence model is highlighted. The influence of the chemistry model is noticeable too. A procedure is described to construct appropriate inlet boundary conditions. Still, the generation of accurate inlet boundary conditions is shown to be far less important, their effect being local, close to the nozzle exit. In the second part of the paper, results are presented with the transported scalar PDF approach as turbulence-chemistry interaction model. A C1 skeletal scheme serves as chemistry model, while the EMST method is applied as micro-mixing model. For the transported PDF simulations, the model for the pilot flames, as an energy source term in the mean enthalpy transport equation, is important with respect to the accuracy of the flow field predictions. It is explained that the strong influence on the flow and mixing field is through the turbulent shear stress force in the region, close to the nozzle exit. © Springer 2005., The first author is Postdoctoral Researcher of the Fund of Scientific Research – Flanders (Belgium) (FWO-Vlaanderen). Part of the work was financed by the Fund of Scientific Research – Flanders (Belgium) (FWO-Vlaanderen) through FWOproject G.0070.03.

This paper presents a numerical modeling study of one ethanol spray flame from the Delft Spray-in-Hot-Coflow (DSHC) database, which has been used to study Moderate or Intense Low-oxygen Dilution (MILD) combustion of liquid fuels (Correia Rodrigues et al. Combust. Flame 162(3), 759–773, 2015). A “Lagrangian-Lagrangian” approach is adopted where both the joint velocity-scalar Probability Density Function (PDF) for the continuous phase and the joint PDF of droplet properties are modeled and solved. The evolution of the gas phase composition is described by a Flamelet Generated Manifold (FGM) and the interaction by exchange with the mean (IEM) micro-mixing model. Effects of finite conductivity on droplet heating and evaporation are accounted for. The inlet boundary conditions starting in the dilute spray region are obtained from the available experimental data together with the results of a calculation of the spray including the dense region using ANSYS Fluent 15. A method is developed to determine a good estimation for the initial droplet temperature. The inclusion of the “1/3” rule for droplet evaporation and dispersion models is shown to be very important. The current modeling approach is capable of accurately predicting main properties, including mean velocity, droplet mean diameter and number density. The gas temperature is under-predicted in the region where the enthalpy loss due to droplet evaporation is important. The flame structure analysis reveals the existence of two heat release regions, respectively having the characteristics of a premixed and a diffusion flame. The experimental and modeled temperature PDFs are compared, highlighting the capabilities and limitations of the proposed model.