A Priori and a Posteriori Analyses of Differential and Preferential Diffusion in Large Eddy Simulations of Partially Premixed Hydrogen-air Flames

Differential diffusion (DD) and non-unity Lewis number (Le) effects in the filtered equations of the mixture fraction, progress variable, their respective sub-grid scale (SGS) variances and enthalpy are investigated using a priori and a posteriori analyses of a lifted turbulent hydrogen jet flame. The a priori analyses show that the absolute magnitudes of the DD terms in the filtered mixture fraction equation and its SGS variance are significant individually, but their net contribution is small. The DD effects are found to be small for the progress variable and its SGS variance. One non-unity Le term is of similar magnitude to the turbulent flux for the filtered enthalpy and is independent of turbulent transport. Therefore, a simple model for this effect is constructed using flamelets. A priori validation of this model is performed using direct numerical simulation data of a lifted hydrogen flame and its a posteriori verification is undertaken through two large eddy simulations. This effect influences the enthalpy field and hence the temperature is affected because of the relative increase (decrease) in thermal diffusivity for lean (rich) mixtures. Hence, higher peak temperatures are observed in the rich mixture when the non-unity Le effects are included. However, its overall effects on the flame lift-off height and flame-brush structure are observed to be small when compared with measurements. Hence, the DD and non-unity Le effects are negligible for LES of partially premixed combustion of hydrogen–air mixtures in high Reynolds number flows. Novelty and significance The relative importance of differential and preferential diffusion effects for large eddy simulations using the tabulated chemistry approach is systematically assessed. The consistency among the complete set of equations and their closure models of the controlling variables (filtered mixture fraction, progress variable, their subgrid scale variances and enthalpy) for partially premixed combustion is maintained on the physical and mathematical grounds for the first time. The novelty of this work lies in the development, validation and verification of a computationally simple, yet accurate and robust, model for these diffusion effects, and its a priori and a posteriori analyses. It is demonstrated that the influence of non-equidiffusion is small for turbulent partially premixed hydrogen–air flames and hence, the standard unity Lewis number approach is shown to be sufficient for turbulent partially premixed flames with high turbulence levels, which are typical in practical applications.