DNS of swirling hydrogen–air premixed flames

•We investigated the effect of turbulence on reaction rate in premixed swirl flames.•PDFs show correlations between the TKE dissipation and reaction rates.•Scalar and velocity gradients have an influence on reaction rate through mixing.•Conventional models complement their limitations, based on the local conditions.•An approach is proposed to exploit advantages of these models using time scales.

Direct numerical simulation is employed to investigate the turbulent flow characteristics and their effect on local flames for mean reaction rate modelling in turbulent swirling premixed flames. Two swirl numbers having significant effects on the formation of a central recirculation zone in the combustor are considered. The large velocity gradients in the higher swirl number case produce high turbulence intensity in a relatively upstream region compared to the lower swirl number case. The conditional Probability Density Functions (PDFs) of the reaction rate and dissipation rates of turbulent kinetic energy and scalar fluctuations are also examined. The PDFs show correlations between the turbulence energy dissipation and reaction rates and between the scalar dissipation and reaction rates, suggesting that the heat and radicals from the hot products trapped in the recirculation zones are mixed with the reactants, not only through scalar dissipation rate (i.e. scalar gradient) but also by small-scale processes of turbulence relevant to turbulent kinetic energy dissipation rate. Therefore, both scalar and velocity gradients have a strong influence on the chemical reactions through mixing of cold reactant and hot products. A conventional flamelet and EDC models are used to estimate the mean reaction rate, and to study the balance between these two mixing mechanisms. Although both models show a qualitative agreement with the DNS results, these models compensate their limitations each other, depending on the local turbulence and thermochemical conditions. A simple approach is proposed to exploit the advantages of these two models by considering the balance of two mixing mechanisms based on the chemical and turbulence time scales. The estimated mean reaction rate using the proposed model is significantly improved for the higher swirl number case, although the estimated value slightly shifts away from the DNS results for the lower swirl number case. The improved modelling estimate and the balance of turbulence and chemical time scales suggest that the locations of intense reaction zones are strongly related to the dissipation rates of both scalar and turbulent kinetic energy.