Nonlinear cellular dynamics of the idealized detonation model: Regular cells

Abstract

High-resolution numerical simulations of cellular detonations are performed using a parallelized adaptive grid solver, in the case where the channel width is very wide. In particular, the nonlinear response of a weakly unstable Zeldovich–Neumann–Doering (ZND) detonation to two-dimensional perturbations is studied in the context of the idealized one-step chemistry model. For random perturbations, cells appear with a characteristic size in good agreement with that corresponding to the maximum growth rate from a linear stability analysis. However, the cells then grow and equilibrate at a larger size. It is also shown that the linear analysis predicts well the ratio of cell lengths to cell widths of the fully developed cells. The evolutionary dynamics of the growth are nonetheless quite slow, in that the detonation needs to run of the order of 1000 reaction lengths before the final size and equilibrium state is reached. For sinusoidal perturbations, it is found that there is a large band of wavelengths/cell sizes which can propagate over very long distances (∼1000 reaction lengths). By perturbing the fully developed cells of each wavelength, it is found that smaller cells in this range are unstable to symmetry breaking, which again results in cellular growth to a larger final size. However, a range of larger cell sizes appear to be nonlinearly stable. As a result it is found that the final cell size of the model is non-unique, even for such a weakly unstable, regular cell case. Indeed, in the case studied, the equilibrium cell size varies by 100% with different initial conditions. Numerical dependencies of the cellular dynamics are also examined.