Direct numerical simulation of the droplet evaporation and combustion using a discontinuous Galerkin scheme

单液滴燃烧的研究是理解、设计和评价燃烧系统性能的重要步骤，也是理解和模拟喷雾燃烧的重要步骤，喷雾燃烧在许多技术系统中起着重要的作用。总的研究目标是开发和实现一个高精度的数值求解器，用于模拟单个燃料液滴在环境流场中的蒸发和燃烧。长期目标是研究燃烧液滴对固体表面的影响以及多个燃烧液滴的影响。为此，采用不连续Galerkin方法(DGM)精确计算了具有非材料变形界面的气液两相流动和气相中化学物质的输运过程。在最近结束的第一个资助期内，开发了低马赫数可压缩流动的单相求解器、物质输运和燃烧的求解器以及不可压缩多相流的求解器。这些是通往我们最终目标的道路上具有挑战性的、必不可少的基石：通过低马赫数近似对单个液滴的燃烧进行数值模拟。用水平集方法结合截面法和非光滑基函数来跟踪流体界面，以表示流动特性的跳跃。另一个重要的方面是提高了求解器的计算性能和网格自适应性。

The study of single droplet combustion is an important step in understanding, designing and evaluating the performance of combustion systems as well as for understanding and modeling spray combustion, which plays a major role in many technical systems. The general research objective is to develop and implement a highly accurate numerical solver for the simulation of the evaporation and combustion of a single fuel droplet in an ambient flow field. The long-term objectives are to investigate the impact of a burning droplet on a solid surface as well as the impact of multiple burning droplets.For this purpose, the Discontinuous Galerkin Method (DGM) is employed to accurately compute two-phase liquid-gas flows with non-material deformable interface and the transport processes of the chemical species in the gas phase. Specifically, it is intended to extend the in-house developed DGM library BoSSS (Bounded Support Spectral Solver) to simulate the droplet combustion.In the recently finished first funding period, the single phase solver for low-Mach number compressible flows, the solver for species transport and combustion and the solver for incompressible multiphase flows have been developed. These represent challenging, essential building blocks on the road towards our ultimate objective: The numerical simulation of the combustion of a single droplet by means of the low-Mach number approximation. The fluid interface is tracked by a level set method combined with the cut-cell method and non-smooth basis functions to represent jumps of the flow properties. A further important aspect is the enhancement of the solver with respect to computational performance and mesh adaptivity.