A generalized level-set/in-cell-reconstruction approach for accelerating turbulent premixed flames

Abstract

An extended numerical technique for the simulation of accelerating turbulent premixed flames in large scale geometries is presented. It is based on a hybrid capturing tracking technique. It resembles a tracking scheme in that the front geometry is explicitly computed using a level-set method. The basic flow properties are provided by solving the compressible flow equations. The flame-flow-coupling is achieved by an in-cell-reconstruction technique. In cells cut by the flame, the discontinuous solution is reconstructed from given cell averages by invoking explicitly some Rankine–Hugoniot type jump conditions. Then the reconstructed states and again the front geometry are used to define accurate effective numerical fluxes across grid cell interfaces intersected by the front during the time step considered. Hence, the scheme also resembles a capturing scheme in that only cell averages of conserved quantities are computed. To be able to model inherently unsteady effects, like quenching, reignition, etc, during flame acceleration, we modified the standard Rankine–Hugoniot jump conditions. A source term appearing in the modified jump conditions is computed by evaluating a suitable functional on the basis of a one-dimensional flame structure module, that is attached in the normal direction to the flame front. This module additionally yields quantities such as the net mass burning rate, necessary for the propagation of the level set, and the specific heat release important for the energy release due to the consumption of fuel. Generally, the flame structure calculation takes into account internal physical effects which are not active in the outer flow but essential for the front motion and its feedback on the surrounding fluid. If a suitable set of different (turbulent) combustion models to compute the flame structure is provided, the new numerical technique allows us to consistently represent laminar deflagrations, fast turbulent deflagrations as well as detonation waves. Supplemented with suitable criteria that capture the essence of a deflagration-to-detonation-transition (DDT), the complete evolution of such an event can be implemented in principle.