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Lagrangian Tracking of Material Surfaces in Reacting Flows

Most technically relevant combustion processes take place in turbulent flows. The interaction between the turbulent flow and the combustion chemistry is still the subject of active research. A more detailed understanding of this is required for developing more efficient combustion devices in the future. As the flame interacts with turbulent vortices, it becomes deformed and curved. This has significant influence on the local flame dynamics, because the curved structure of the flame leads to a change in diffusive fluxes. The direct numerical simulation of these phenomena constitutes a computational challenge due to the large range of time and length scales relevant for the combustion process. Additionally, many chemical reactions and intermediate species have to be considered. One approach for studying the complex coupling of the flame and turbulent flow is the Lagrangian tracking of material points on the flame’s surface. Chemical reactions occur in flames in a thin region, which can often be approximated as a two-dimensional surface defined by an iso-surface of e.g. temperature or the mass fraction of chemical species. The movement of this iso-surface can be used to describe the movement of the flame itself, which is caused by two effects: convection with the fluid flow and movement due to an intrinsic velocity, which is called burning velocity or displacement speed. In this work, a new Lagrangian particle type, called flame particle, has been developed in the framework of OpenFOAM, which tracks points on prescribed iso-surfaces and acts as an inert, massless virtual particle. In contrast to fluid particles, which follow the fluid flow and therefore track instantaneous streamlines, the flame particle moves with a combination of the fluid velocity and the burning velocity of the flame, thereby following the flame. The trajectories of these flame particles give insight into the change in thermo-chemical state during the interaction of the turbulent flow and the flame. Additionally, the tracking of material points allows studying time series of different flame properties and reveals memory effects, which could otherwise not be investigated. Because the flames have to be fully resolved in the simulation to apply the new particle tracking, direct numerical simulations are necessary to capture all details of the flame. Therefore, a computationally efficient approach has been developed which utilizes an analytical expression to find intersections of flame particle trajectories with the iso-surface based on a formulation in barycentric coordinates. The computational overhead of the tracking in a testcase of a turbulent flame with 100 million cells and 10 million flame particles simulated with 10000 CPU cores on Germany’s largest supercomputer was 20%. The newly developed flame particles are also applied to a case consisting of a two-dimensional planar flame in laminar flow. Two counter-rotating vortices are generated in front of the flame. As they move through the flame, they deform it, leading to local extinction of the flame. The flame particles are used to systematically study the interaction of the flame and the vortices by tracking diffusive fluxes and chemical reaction rates during the deformation process.