Numerical Simulation of the Cellular Structure of a Weakly Unstable Detonation Wave using PPM Method and Riemann Exact Solver

In this paper, the requirements of accurate simulation of the cellular structure and triple wave configuration of a weakly unstable detonation wave have been studied. Two-dimensional reactive Euler equations and a one-step Arrhenius form chemical mechanism have been solved using the well-known PPM scheme and the exact Riemann solver for a gas mixture of H2/O2/Ar. Introducing harmonic density perturbation ahead of ZND profile, detonation wave with regular structure would be produced. The flow field is restricted to a narrow patch containing detonation wave and moves with it during time and along the channel. Using the narrow patch, instead of the entire channel, leads to enormous computational cost and time saving, without losing the accuracy. At the first step, grid resolution study was conducted. Using the mentioned scheme and one-step chemical mechanism, it was shown that for capturing the cellular structure properly, a grid resolution of about 24 points per half reaction length is required. At the next step, the effects of initial perturbation parameters including perturbation amplitude factor, distance from perturbation to downstream boundary condition and perturbation thickness on the evolution and final cellular structure was examined. This way, permitted domain of variation for the parameters mentioned with the aim of precise simulation of celluar structure would be achieved. Finally, increasing the grid resolutions up to 36 points per half reaction length, capability of one-step Arrhenius chemical mechanism for capturing the second triple-point and the shear layer in triple-wave configuration has been investigated.