Modelling differential diffusion using sparse particle methods

在分子尺度上，扩散是控制混合成分和燃烧过程动力学的关键机制之一。由于分子大小的不同，物质以不同的速度扩散（微分扩散），这导致了相反的等扩散情况——物质的非相关性，从而导致了不同的点火特性、火焰结构和火焰动力学。尽管有充分的证据表明这些影响，但绝大多数燃烧模拟都假设了相同的扩散系数。这是由主导湍流混合的假设来证明的，与微分扩散的影响相反。相反，模拟和实验之间的差异通常可以通过微分扩散来证明：然而，这仍然是假设的，因为由于缺乏令人信服的模型来关闭湍流火焰中的微分扩散效应，因此无法给出证据。碳减少甚至无碳燃烧使得不同运输特性的话题再次及时和热门。不仅是富氢燃烧（例如氢气加入我们的天然气供应网络），而且基于含氮燃料的替代概念也依赖氢气作为真正的能量载体。最重要的是氢，由于它的小分子尺寸，对微分扩散有重要贡献。因此，精确的微分扩散建模策略的发展似乎至关重要，但它远非微不足道，因为湍流混合与分子扩散相互作用。提议的工作现在将在随机稀疏粒子方法的背景下解决微分扩散效应的建模。随机蒙特卡罗粒子表示流体单元的瞬时和局部解，允许跟踪流体单元的历史，并且可以考虑湍流和分子混合的不同局部效应及其“积分”特性。这些模型应借助非反应流和反应流的统计零和一维直接数值模拟（DNS）来开发。初始的零维DNS设置允许分离描述物种输运方程中扩散（以及微分扩散）的不同术语的模型开发。在最后一步，将模型与一系列湍流扩散火焰中物种质量分数的高质量实验数据进行比较，以验证模型的有效性，并在这些数据中测量了微分扩散效应。

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.