The physical mechanism leading to flame local extinction remains a key issue to be further understood. An analysis of large eddy simulation (LES) data with presumed probability density function (PDF) based closure (Chen et al., 2020, Combust. Flame, vol. 212, pp. 415) indicated the presence of localised breaks of the flame front along the stoichiometric line. These observations and their relation to local quenching of burning fluid particles, together with the possible physical mechanisms and conditions allowing their appearance in LES with a simple flamelet model, are investigated in this work using a combined Lagrangian-Eulerian analysis. The Sidney/Sandia piloted jet flames with compositionally inhomogeneous inlet and increasing bulk speeds, amounting to respectively 70 and 90% of the experimental blow-off velocity, are used for this analysis. Passive flow tracers are first seeded in the inlet streams and tracked for their lifetime. The critical scenario observed in the Lagrangian analysis, i.e., burning particles crossing extinction holes on the stoichiometric iso-surface, is then investigated using the Eulerian control-volume approach. For the 70% blow-off case the observed flame front breaks/extinction holes are due to cold and inhomogeneous reactants that are cast onto the stoichiometric iso-surface by large vortices initiated in the jet/pilot shear layer. In this case an extinction hole forms only when the strain effect is accompanied by strong subgrid mixing. This mechanism is captured by the unstrained flamelets model due to the ability of the LES to resolve large-scale strain and considers the SGS mixture fraction variance weakening effect on the reaction rate through the flamelet manifold. Only at 90% blow-off speed the expected limitation of the underlying combustion model assumption become apparent, where the amount of local extinctions predicted by the LES is underestimated compared to the experiment. In this case flame front breaks are still observed in the LES and are caused by a stronger vortex/strain interaction yet without the aid of mixture fraction variance. The reasons for these different behaviours and their implications from a physical and modelling point of view are discussed in this study.@en

Moderate or Intense Low-oxygen Dilution (MILD) combustion allows prevention of the thermo-chemical conditions prone to the formation of pollutant species while ensuring high energy efficiency and fuel flexibility. MILD combustion is characterized by a strong competition between turbulent mixing and chemical kinetics so that turbulence-chemistry interactions are naturally strengthened and unsteady phenomena such as local extinction and re-ignition may occur. The underlying physical mechanisms are not fully understood yet and the validation of combustion models featuring enhanced predictive capabilities is required. Within this context, high-fidelity data from direct numerical simulation (DNS) represent a great opportunity for the assessment and the validation of combustion closure formulations. In this study, the performance of the partially stirred reactor (PaSR) combustion model in MILD conditions was a priori assessed on DNS of turbulent combustion of MILD mixtures in a cubical domain. Modeled quantities of interest, such as heat release rate and reaction rates of major and minor species, were compared to the corresponding filtered quantities extracted from the DNS. The filtered chemical source terms of three main species, CH4, CO2, and CO, and the intermediate OH, were considered. Different submodels for the key model parameters, i.e., the chemical time scale τc and the mixing time scale τmix, were considered and their influence on the results was evaluated. The results revealed that the mixing time scale is the leading scale in the investigated cases. The best agreement with the DNS data regarding the prediction of heat release rate and chemical source terms was achieved by the PaSR model that uses a local dynamic approach for the estimation of the mixing time scale. An overestimation of the OH species source terms occurred in limited zones of the computational domain, characterized by low heat release rates.@en

Moderate or Intense Low-oxygen Dilution (MILD) combustion allows prevention of the thermo-chemical conditions prone to the formation of pollutant species while ensuring high energy efficiency and fuel flexibility. MILD combustion is characterized by a strong competition between turbulent mixing and chemical kinetics so that turbulence-chemistry interactions are naturally strengthened and unsteady phenomena such as local extinction and re-ignition may occur. The underlying physical mechanisms are not fully understood yet and the validation of combustion models featuring enhanced predictive capabilities is required. Within this context, high-fidelity data from direct numerical simulation (DNS) represent a great opportunity for the assessment and the validation of combustion closure formulations. In this study, the performance of the partially stirred reactor (PaSR) combustion model in MILD conditions was a priori assessed on DNS of turbulent combustion of MILD mixtures in a cubical domain. Modeled quantities of interest, such as heat release rate and reaction rates of major and minor species, were compared to the corresponding filtered quantities extracted from the DNS. The filtered chemical source terms of three main species, CH4, CO2, and CO, and the intermediate OH, were considered. Different submodels for the key model parameters, i.e., the chemical time scale τc and the mixing time scale τmix, were considered and their influence on the results was evaluated. The results revealed that the mixing time scale is the leading scale in the investigated cases. The best agreement with the DNS data regarding the prediction of heat release rate and chemical source terms was achieved by the PaSR model that uses a local dynamic approach for the estimation of the mixing time scale. An overestimation of the OH species source terms occurred in limited zones of the computational domain, characterized by low heat release rates.@en

Moderate or Intense Low-oxygen Dilution (MILD) combustion allows prevention of the thermo-chemical conditions prone to the formation of pollutant species while ensuring high energy efficiency and fuel flexibility. MILD combustion is characterized by a strong competition between turbulent mixing and chemical kinetics so that turbulence-chemistry interactions are naturally strengthened and unsteady phenomena such as local extinction and re-ignition may occur. The underlying physical mechanisms are not fully understood yet and the validation of combustion models featuring enhanced predictive capabilities is required. Within this context, high-fidelity data from direct numerical simulation (DNS) represent a great opportunity for the assessment and the validation of combustion closure formulations. In this study, the performance of the partially stirred reactor (PaSR) combustion model in MILD conditions was a priori assessed on DNS of turbulent combustion of MILD mixtures in a cubical domain. Modeled quantities of interest, such as heat release rate and reaction rates of major and minor species, were compared to the corresponding filtered quantities extracted from the DNS. The filtered chemical source terms of three main species, CH4, CO2, and CO, and the intermediate OH, were considered. Different submodels for the key model parameters, i.e., the chemical time scale τc and the mixing time scale τmix, were considered and their influence on the results was evaluated. The results revealed that the mixing time scale is the leading scale in the investigated cases. The best agreement with the DNS data regarding the prediction of heat release rate and chemical source terms was achieved by the PaSR model that uses a local dynamic approach for the estimation of the mixing time scale. An overestimation of the OH species source terms occurred in limited zones of the computational domain, characterized by low heat release rates.@en

Moderate or Intense Low-oxygen Dilution (MILD) combustion allows prevention of the thermo-chemical conditions prone to the formation of pollutant species while ensuring high energy efficiency and fuel flexibility. MILD combustion is characterized by a strong competition between turbulent mixing and chemical kinetics so that turbulence-chemistry interactions are naturally strengthened and unsteady phenomena such as local extinction and re-ignition may occur. The underlying physical mechanisms are not fully understood yet and the validation of combustion models featuring enhanced predictive capabilities is required. Within this context, high-fidelity data from direct numerical simulation (DNS) represent a great opportunity for the assessment and the validation of combustion closure formulations. In this study, the performance of the partially stirred reactor (PaSR) combustion model in MILD conditions was a priori assessed on DNS of turbulent combustion of MILD mixtures in a cubical domain. Modeled quantities of interest, such as heat release rate and reaction rates of major and minor species, were compared to the corresponding filtered quantities extracted from the DNS. The filtered chemical source terms of three main species, CH4, CO2, and CO, and the intermediate OH, were considered. Different submodels for the key model parameters, i.e., the chemical time scale τc and the mixing time scale τmix, were considered and their influence on the results was evaluated. The results revealed that the mixing time scale is the leading scale in the investigated cases. The best agreement with the DNS data regarding the prediction of heat release rate and chemical source terms was achieved by the PaSR model that uses a local dynamic approach for the estimation of the mixing time scale. An overestimation of the OH species source terms occurred in limited zones of the computational domain, characterized by low heat release rates.@en

Moderate or Intense Low-oxygen Dilution (MILD) combustion allows prevention of the thermo-chemical conditions prone to the formation of pollutant species while ensuring high energy efficiency and fuel flexibility. MILD combustion is characterized by a strong competition between turbulent mixing and chemical kinetics so that turbulence-chemistry interactions are naturally strengthened and unsteady phenomena such as local extinction and re-ignition may occur. The underlying physical mechanisms are not fully understood yet and the validation of combustion models featuring enhanced predictive capabilities is required. Within this context, high-fidelity data from direct numerical simulation (DNS) represent a great opportunity for the assessment and the validation of combustion closure formulations. In this study, the performance of the partially stirred reactor (PaSR) combustion model in MILD conditions was a priori assessed on DNS of turbulent combustion of MILD mixtures in a cubical domain. Modeled quantities of interest, such as heat release rate and reaction rates of major and minor species, were compared to the corresponding filtered quantities extracted from the DNS. The filtered chemical source terms of three main species, CH4, CO2, and CO, and the intermediate OH, were considered. Different submodels for the key model parameters, i.e., the chemical time scale τc and the mixing time scale τmix, were considered and their influence on the results was evaluated. The results revealed that the mixing time scale is the leading scale in the investigated cases. The best agreement with the DNS data regarding the prediction of heat release rate and chemical source terms was achieved by the PaSR model that uses a local dynamic approach for the estimation of the mixing time scale. An overestimation of the OH species source terms occurred in limited zones of the computational domain, characterized by low heat release rates.@en

Moderate or Intense Low-oxygen Dilution (MILD) combustion allows prevention of the thermo-chemical conditions prone to the formation of pollutant species while ensuring high energy efficiency and fuel flexibility. MILD combustion is characterized by a strong competition between turbulent mixing and chemical kinetics so that turbulence-chemistry interactions are naturally strengthened and unsteady phenomena such as local extinction and re-ignition may occur. The underlying physical mechanisms are not fully understood yet and the validation of combustion models featuring enhanced predictive capabilities is required. Within this context, high-fidelity data from direct numerical simulation (DNS) represent a great opportunity for the assessment and the validation of combustion closure formulations. In this study, the performance of the partially stirred reactor (PaSR) combustion model in MILD conditions was a priori assessed on DNS of turbulent combustion of MILD mixtures in a cubical domain. Modeled quantities of interest, such as heat release rate and reaction rates of major and minor species, were compared to the corresponding filtered quantities extracted from the DNS. The filtered chemical source terms of three main species, CH4, CO2, and CO, and the intermediate OH, were considered. Different submodels for the key model parameters, i.e., the chemical time scale τc and the mixing time scale τmix, were considered and their influence on the results was evaluated. The results revealed that the mixing time scale is the leading scale in the investigated cases. The best agreement with the DNS data regarding the prediction of heat release rate and chemical source terms was achieved by the PaSR model that uses a local dynamic approach for the estimation of the mixing time scale. An overestimation of the OH species source terms occurred in limited zones of the computational domain, characterized by low heat release rates.@en

Subgrid correlation of mixture fraction, Z, and progress variable, c, is investigated using direct numerical dimulation (DNS) data of a hydrogen lifted jet flame. Joint subgrid behaviour of these two scalars are obtained using a Gaussian-type filter for a broad range of filter sizes. A joint probability density function (JPDF) constructed using single-snapshot DNS data is compared qualitatively with that computed using two independent β-PDFs and a copula method. Strong negative correlation observed at different streamwise locations in the flame is captured well by the copula method. The subgrid contribution to the Z–c correlation becomes important if the filter is of the size of the laminar flame thickness or larger. A priori assessment for the filtered reaction rate using the flamelet approach with independent β-PDFs and correlated JPDF is then performed. Comparison with the DNS data shows that both models provide reasonably good results for a range of filter sizes. However, the reaction rate computed using copula JPDF is found to have a better agreement with the DNS data for large filter sizes because the subgrid Z–c correlation effect is included.@en

Subgrid correlation of mixture fraction, Z, and progress variable, c, is investigated using direct numerical dimulation (DNS) data of a hydrogen lifted jet flame. Joint subgrid behaviour of these two scalars are obtained using a Gaussian-type filter for a broad range of filter sizes. A joint probability density function (JPDF) constructed using single-snapshot DNS data is compared qualitatively with that computed using two independent β-PDFs and a copula method. Strong negative correlation observed at different streamwise locations in the flame is captured well by the copula method. The subgrid contribution to the Z–c correlation becomes important if the filter is of the size of the laminar flame thickness or larger. A priori assessment for the filtered reaction rate using the flamelet approach with independent β-PDFs and correlated JPDF is then performed. Comparison with the DNS data shows that both models provide reasonably good results for a range of filter sizes. However, the reaction rate computed using copula JPDF is found to have a better agreement with the DNS data for large filter sizes because the subgrid Z–c correlation effect is included.@en

Subgrid correlation of mixture fraction, Z, and progress variable, c, is investigated using direct numerical dimulation (DNS) data of a hydrogen lifted jet flame. Joint subgrid behaviour of these two scalars are obtained using a Gaussian-type filter for a broad range of filter sizes. A joint probability density function (JPDF) constructed using single-snapshot DNS data is compared qualitatively with that computed using two independent β-PDFs and a copula method. Strong negative correlation observed at different streamwise locations in the flame is captured well by the copula method. The subgrid contribution to the Z–c correlation becomes important if the filter is of the size of the laminar flame thickness or larger. A priori assessment for the filtered reaction rate using the flamelet approach with independent β-PDFs and correlated JPDF is then performed. Comparison with the DNS data shows that both models provide reasonably good results for a range of filter sizes. However, the reaction rate computed using copula JPDF is found to have a better agreement with the DNS data for large filter sizes because the subgrid Z–c correlation effect is included.@en

Large eddy simulation (LES) paradigms are used in the present work to predict premixed and partially premixed turbulent flames with flamelets based thermochemistry and presumed filtered density function approach for turbulence-chemistry interaction modelling. The combustion model requires a closure for the scalar dissipation rate of a progress variable, in which a modelling constant must be chosen. The present work focuses on the computation of the model constant through dynamic procedures based on the scale-similarity assumption, which requires the application of test-filters. In particular, two test-filtering approaches for LES, based respectively on an algebraic formulation and a newly proposed differential equation, are tested for flame configurations at different levels of turbulence, and using block-structured and unstructured meshes. The analysis shows that the differential filter, unlike the algebraic one, is handled well in situations of weak turbulence at comparable computational costs. At higher turbulence conditions the outcome looks less dependent on the test-filter and mesh topology used, although quantitative differences in the behaviour of the dynamically-computed model constant are still observable and discussed. Further analyses to understand the behaviour of the two filters are presented in the paper.@en

Large eddy simulation (LES) paradigms are used in the present work to predict premixed and partially premixed turbulent flames with flamelets based thermochemistry and presumed filtered density function approach for turbulence-chemistry interaction modelling. The combustion model requires a closure for the scalar dissipation rate of a progress variable, in which a modelling constant must be chosen. The present work focuses on the computation of the model constant through dynamic procedures based on the scale-similarity assumption, which requires the application of test-filters. In particular, two test-filtering approaches for LES, based respectively on an algebraic formulation and a newly proposed differential equation, are tested for flame configurations at different levels of turbulence, and using block-structured and unstructured meshes. The analysis shows that the differential filter, unlike the algebraic one, is handled well in situations of weak turbulence at comparable computational costs. At higher turbulence conditions the outcome looks less dependent on the test-filter and mesh topology used, although quantitative differences in the behaviour of the dynamically-computed model constant are still observable and discussed. Further analyses to understand the behaviour of the two filters are presented in the paper.@en

Large eddy simulation (LES) paradigms are used in the present work to predict premixed and partially premixed turbulent flames with flamelets based thermochemistry and presumed filtered density function approach for turbulence-chemistry interaction modelling. The combustion model requires a closure for the scalar dissipation rate of a progress variable, in which a modelling constant must be chosen. The present work focuses on the computation of the model constant through dynamic procedures based on the scale-similarity assumption, which requires the application of test-filters. In particular, two test-filtering approaches for LES, based respectively on an algebraic formulation and a newly proposed differential equation, are tested for flame configurations at different levels of turbulence, and using block-structured and unstructured meshes. The analysis shows that the differential filter, unlike the algebraic one, is handled well in situations of weak turbulence at comparable computational costs. At higher turbulence conditions the outcome looks less dependent on the test-filter and mesh topology used, although quantitative differences in the behaviour of the dynamically-computed model constant are still observable and discussed. Further analyses to understand the behaviour of the two filters are presented in the paper.@en

A cyclonic burner operating under moderate or intense low-oxygen dilution (MILD) conditions is simulated using a perfectly stirred reactor (PSR) incorporated within a tabulated chemistry approach. A presumed joint probability density function method is used with appropriate submodels for the turbulence-chemistry interaction. Non-adiabatic effects are included in the PSR calculation to take into account the effects of non-negligible wall heat loss in the burner. Five different operating conditions are investigated, and the computed mean temperatures agree well with measurements. A substantial improvement is observed when the non-adiabatic PSR is used, highlighting the importance of heat transfer effects for burner configurations involving internal exhaust gas recirculation. Furthermore, enhanced reaction homogeneity is observed in this cyclonic configuration for the globally lean case, leading to a more spatially uniform temperature variation with MILD combustion.@en