Flame front capturing/tracking schemes for compressible and incompressible reactive flow

Abstract

We present hybrid capturing/tracking methods for the simulation of turbulent premixed flames in meso- and large-scale geometries. Such schemes resemble a tracking schemes in that the flame front is explicitly computed and propagated using a level set method. The flame-flow-coupling uses incell-reconstruction. In cut cells, burnt and unburned states are reconstructed from given cell-averages and Rankine-Hugoniot jump conditions. Using burned and unburned states together with the local front geometry to define accurate numerical fluxes in a conservative finite volume method, the scheme resembles a capturing scheme as well. Quasi one-dimensional turbulent flame structure models can be attached in normal direction to the flame front in a modular fashion. This paper summarizes the key features of such algorithms from an incompressible and compressible point of view. Recent developments will be explained, including tabulated detailed chemistry and direct incorporation of physical jump conditions into the numerical discretisation. These methods allow simulations of unsteady phenomena, such as quenching, ignition, and thermoacoustic instabilities. Combustion in many technical devices as gas turbines usually takes places at a low Mach number where compressibility effects are negligible. An asymptotic analysis of the reactive flow equations in the zero Mach number limit motivates new ideas for flame capturing/tracking schemes in this regime. Exemplary results illustrating the capability of the extended capturing/tracking idea are provided, including acoustic forcing of cold zero Mach number flow, freely propagating flames over obstacles, turbulent flames in laboratory setups, and the behavior of unsteady turbulent flame structures.