Bifurcation of the characteristic cells into multiple smaller cells and decay of those cells into single large characteristic cell is observed frequently. In the present study the bifurcation phenomenon of the detonation front is investigated for marginally unstable detonations using decomposition technique. Numerical analysis is carried out with detailed chemical kinetics for detonation propagation in H2/O2 mixtures at 10 kPa. The dynamic characteristics of the instability at the detonation front, such as the local oscillation frequency and the coherent spatial structure of the oscillation are also studied with dynamic mode decomposition (DMD) technique. The coherent structures of the primary and secondary detonation cells are analyzed during the cell bifurcation process and the mechanism in which the secondary cells are formed is investigated. It is demonstrated that the modal analysis categorizes the instability phenomena clearly and can be effectively utilized to identify the origin and source of the instability.

An unstable shock-induced combustion (SIC) case around a hemispherical projectile has been numerically studied which experimentally produced a regular oscillation. Comparison of detailed H2/O2 reaction mechanisms is made for the numerical simulation of SIC with higher-order numerical schemes intended for the use of the code for the hypersonic propulsion and supersonic combustion applications. The simulations show that specific reaction mechanisms are grid-sensitive and produce spurious reactions in the high-temperature region, which trigger artificial instability in the oscillating flow field. The simulations also show that specific reaction mechanisms develop such spurious oscillations only at very fine grid resolutions. The instability mechanism is investigated using the dynamic mode decomposition (DMD) technique and the spatial structure of the decomposed modes are further analyzed. It is found that the instability triggered by the high-temperature reactions strengthens the reflecting compression wave and pushes the shock wave further and disrupts the regularly oscillating mechanism. The spatial coherent structure from the DMD analysis shows the effect of this instability in different regions in the regularly oscillating flow field.