Numerical study on cellular detonation in a straight tube based on detailed chemical reaction model

Cellular detonation in a straight tube was numerically studied, based on two-dimensional reactive Euler equations and detailed chemical reaction model. The 5th order WENO scheme was employed to resolve the convective terms, and the additive semi-implicit Runge-Kutta methods was used to treat the stiffness caused by the chemical source terms. The contours of density, pressure, temperature and typical species mass fraction as well as numerical cellular pattern etc. were obtained. The results show that, the different grid resolutions evidently influence the regularity of detonation cells and the equilibrium detonation mode number. As grid size increases, the detonation wave developes more irregular cells and more additional triple points. For the given gas mixtures, initial pressure, initial temperature and tube width, the final self-sustaining detonation mode number is converged to a fixed value. It is also independent of the variety of initial perturbations, provided that the initial perturbations are sufficiently strong to reproduce the self-sustaining cellular detonation. Detonation velocity ranges from 0.88DCJ to 1.5DCJ along the cell centerline, and the average detonation speed is only 0.88% different from the CJ value. The ratio of peak pressure to initial pressure ranges from 14 to 50 along the cell centerline. The average detonation speed and cell aspect ratio are remarkably agreeable with experimental values, but the computational cells are slightly smaller than the experimental cells. Some complicated detonation physics including transverse waves, un-reacted gas pocket, re-initiation of detonation cells etc. was recognized.