Modelling differential diffusion using sparse particle methods

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Diffusion is one of the key mechanisms that govern – at molecular scale - the mixture composition and therefore the dynamics of combustion processes. Due to the varying size of the molecules, species diffuse at different velocities (differential diffusion) and this leads to -opposite equal diffusivity cases – a decorrelation of species and therefore to different ignition characteristics, flame structures and flame dynamics. Despite ample evidence of these effects, the vast majority of combustion simulations assumes equal diffusivities. This is justified by the assumption of dominant turbulent mixing the opposes the effects of differential diffusion. Conversely, differences between simulations and experiments are often justified by differential diffusion: this, however, remains hypothetical as proof cannot be given due to a lack of convincing models for closure of differential diffusion effects in turbulent flames.Carbon reduced or even carbon-free combustion renders the topic of varying transport characteristics once again timely and topical. Not only hydrogen enriched combustion (e.g. hydrogen addition to our natural gas supply networks) but also alternative concepts based on e.g. nitrogen containing fuels rely on hydrogen as the real energy carrier. And it is foremost hydrogen that significantly contributes to differential diffusion due to its small molecule size.The development of accurate modelling strategies for differential diffusion seems therefore crucial, but it is far from being trivial as turbulent mixing interacts with molecular diffusion. The proposed work will now address the modelling of differential diffusion effects in the context of a stochastic sparse particle method. The stochastic Monte-Carlo particles represent an instantaneous and local solution of a fluid element and allow for tracking the history of a fluid element, and the varying local Effects of turbulent and molecular mixing and their “integral” character can be considered.The models shall be developed with the aid of statistically zero- and one-dimensional direct numerical simulations (DNS) of non-reacting and reacting flows. The initial zero-dimensional DNS setups allow for a separation of the model development for the different terms that describe diffusion (and also differential diffusion) in the species transport equations. In a final step, the models shall be validated by comparison of simulations with high quality experimental data of species mass fractions in a series of turbulent diffusion flames where differential diffusion effects were measured.