Towards a Generalized Level-Set/In-Cell Reconstruction Approach for Accelerating Turbulent Premixed Flames

Abstract

Due to the feedback between turbulence, gas expansion and flame front dynamics a continuous acceleration of premixed flames can occur. This process occurs, e.g., in large scale gas explosions and astrophysical nova- and supernova explosions. In the context of flame accelerations and DDT one is faced with rapidly changing thermodynamic, mean flow and turbulence conditions. One consequence is that the internal structure of the propagating combustion front will become inherently time dependent. In addition, the turbulence intensities associated with the accelerating flow will increase and grow rapidly beyond the characteristic burning velocity of a laminar flame. While turbulence intensities are still low, quasi laminar combustion takes place in thin ``flamelets''. Turbulent combustion modelling will in this case aim at a description of the net flame surface area and of the mean quasi-laminar burning velocity in order to arrive at the net rate of unburnt gas consumption. If, on the other hand, turbulence intensities increase dramatically, then the turbulence-induced strains will locally distort the flamelet structures or even quench them completely and a more stochastic interaction between reaction, turbulent transport and diffusion becomes significant. As a consequence in these regimes, the ``thin-reaction-zone regime'' and the ``well-stirred reactor'' regime, very different effective turbulent combustion models must be employed. Here we present a new numerical technique which---given such a set of (turbulent) combustion models allows us to consistently represent laminar deflagrations, fast turbulent deflagrations as well as detonation waves. Supplemented with suitable DDT criteria, the complete evolution of a DDT process can be implemented in principle.