Lagrangian characterization of induction and reaction timescales in a cellular gaseous detonation

A Lagrangian approach was proposed to analyze induction and reaction times in the cellular gaseous detonation. Two-dimensional simulations in an argon-diluted and non-diluted hydrogen-based mixtures were performed with detailed chemistry, along particle trajectories. The distribution of the induction and reaction times inside the cell was significantly different between the Eulerian and the Lagrangian perspectives, the latter showing non-monotonic behavior. Preferential thermodynamic paths laid along the Rankine–Hugoniot curve and behind transverse waves (TW). All particles were ignited within half and one cell cycle for the diluted and non-diluted mixture, respectively. The ignition mechanisms were not only one-dimensional, but also multi-dimensional, with ignition behind the TW being the most important, and collision of TW and triple points being secondary. A new topology inside the cell could be drawn, from the intersection of the ignition front with TW. TW appeared as phase waves in the (x,t) diagram. Comparison of H2O mass fraction between local and equilibrium values indicated that a local chemical disequilibrium remained (superequilibrium), due to TW. Equating the mean sonic plane with thermochemical equilibrium in the non-diluted case is not completely accurate. Furthermore, the characteristic time scales for chemical and hydrodynamic phenomena were compared. The diffusive phenomenon did not make any contribution in the mixtures tested. In comparison with the Zel'dovich–von Neumann–Döring model, a shorter average induction time was found in the non-diluted mixture, which is not in line with the results from previous Favre approaches. The average reaction time was also shorter in both mixtures.