The computations show that as the critical instant is approached the flame speed remains finite while its acceleration becomes unbounded, with the event emitting a well-defined disturbance into the flow field ahead of the flame. Computations have not yet been taken beyond the critical event, but a hypothesis suggested by the experimentally observed phenomenon of galloping flames is that the flame will then slow immediately at the critical event - before the process, qualitatively, begins to repeat itself. The mathematical model developed for this set-up and the interpretation of its solution are described below. This work is joint with John Starkenberg of US Army Research Laboratory Aberdeen MD and has been funded by Army Research Lab through Batelle. In this work we are extending the front tracking method to include initiation of detonation waves using a discrete mixture equation of state.
Detonation waves are very fast, sharp and strong.
A shock wave heats up an explosive material, following which, the material decomposes at a rate which depends on the temperature, pressure and possibly on the pressure to which the explosive is initially shocked. Thus, it is extremely important not to smear the shock wave in order to get an accurate initial pressure. The front tracking numerical method enables one to compute an accurate location for the shock wave in time as well as the fluid state behind the wave. Once combustion is initiated, the reaction proceeds and the material is modeled using a combination of the unreacted and reacted equations of state treating the material as a discrete mixture. In the figure, we present an example of a shock initiating a detonation on the right and we see the buildup of the density over time as the detonation wave proceeds through the explosive.