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

A simple model based on a Perfectly Stirred Reactor (PSR) was proposed for moderate or intense low-oxygen dilution (MILD) combustion. The PSR calculation covers the entire flammability range and the tabulated chemistry approach was applied with a presumed joint probability density function (PDF). The jet in hot and diluted coflow experimental set-up under MILD conditions was simulated using PSR model for two oxygen dilution levels. The unheated fuel jet consists of 50% CH4 and 50% H2. The computed results for mean temperature major and minor species mass fractions were compared with the experimental data and simulation results through a multi-environment transported PDF approach. A good agreement was observed at three different axial locations for these comparisons despite peak value overprediction of CO formation suggesting that MILD combustion can be effectively modeled by the proposed PSR model with lower computational cost.@en